Here is a list of the Old Testament passages which Paul quotes from

Romans 3:10-12 from Psalm 14:1-3 and Psalm 53:1-3
Romans 3:13 from Psalm 5:9 and Psalm 140:3
Romans 3:14 from Psalm 10:7
Romans 3:15-17 from Isaiah 59:7-8 and see Isaiah 48:22
Romans 3:18 from Psalm 36:1

Paul has just said all men are "under (the power of) sin" (See notes). In this section it is as if he says "Are you still not convinced? Let me show you further proof the Old Testament!" He is bringing his arguments to a climax demonstrating that the totally sinful state of both the Jew and the Gentile is repeatedly confirmed by the testimony of the Scriptures. Paul begins by quoting from Psalm 14:1-3 which shows the universality ("no one...good...all turned aside") of sin.

Middletown Bible has the following outline of next section:

 Romans 3:9 -THE CHARGE -- All are under sin.

Romans 3:10-18 -THE INDICTMENT. An indictment is a formal written statement framed by a prosecuting authority (in this case, GOD HIMSELF) charging a person with an offense.

Romans 3:19 - THE VERDICT - GUILTY!

Paul as in a judicial procedure is bringing an indisputable, "air tight"  indictment against both the Jews and the Gentiles.

The KJV Bible Commentary explains that...

An indictment is then a formal, written charge and every indictment must have at least one count, one specific charge to it. The more serious the crime, the more counts to the indictment. Paul immediately follows this pattern by quoting from a series of Old Testament passages which demonstrate, in no less than fourteen counts, the perversity and depravity of the entire world. (Dobson, E G, Charles Feinberg, E Hindson, Woodrow Kroll, H L. Wilmington: KJV Bible Commentary: Nelson)

Newell subtitles Romans 3:10-18 as "Fourteen Horrible Things about All Men" and observes that we find God speaking...

in these fourteen counts first, as a Judge: Ro 3:10, 11, 12; next, as a Physician: Ro 3:13, 14, 15; and third, as a Divine Historian: Ro 3:16, 17, 18... This awful list of fourteen facts about the human race, quoted from the Old Testament Scriptures, describes, of course, humanity as it is by nature. Therefore if we have believed the Gospel, and are thus righteous before God in Christ, we have double reason to study these truths: first, that we may by understanding the facts, as God sees them, about ourselves, have a correct estimate of humanity, which, of course, unenlightened men never gain; and, second, that we may be constantly moved to give praise to God for His measureless grace that reached even such as we were! (Romans 3: Sermons)

It is written (1125) (grapho from root graph- = primarily means to scratch on or engrave as on an ornament, reports, letters, etc; English = graph, graphic, etc) means to engrave or inscribe with a pen or stylus characters or letters on a surface which can be wood, wax, metal, leather, stone, parchment, dirt (John ), paper, etc. (Click to review all 191 uses of grapho in the NAS)

It is written should put a stop to every complaint or excuse. Paul is saying don't judge but remember you will appear before Me to give an account (as the next verse clarifies). This sobering thought should motivate us to obey this injunction.

The perfect tense indicates that this is a completed state and reflects the permanence of the written Word (cp Mt 24:35, Pr 30:5 Isa 40:8, 1Pe 1:23, 24, 25-notes). The idea is that "It has been written, with the present result that it is on record" or "it stands written".  The perfect tense then speaks of permanence and reflects the truth echoed by David when he wrote...

"Forever, O LORD, Thy word is settled in heaven." (Ps 119:89-Spurgeon's Note).

The following section (Ro 3:10-20) is a veritable scriptural resume and demonstration of the condemnation of all men, both Jews and Gentiles.

Are there no exceptions? Paul answers quite sharply in (Ro 3:10, 11, 12) with a barrage of negatives,

“There is none … not even one… none … none … not even one.”

Paul now will demonstrate that by nature all people, without exception, are under the power, mastery and authority of Sin. Notice that in order to do so, he does not choose to remind his readers of the gross immorality that marked the pagan culture. Why not? Because doubtless many a Jew and even a few "moral" Gentiles might object saying 

“I, for one, am not guilty of those gross sins!”

Instead Paul, like Jesus in the Sermon on the Mount, goes to the "heart" of the matter, initially selecting man's tongue, fully aware that the tree is known by its fruit, for out of the mouth comes that which fills the heart (cp Mt 15:16, 17, 18, 19, 20, Mk 7:21, 22, 23, Ge 6:5, 8:21, Job15:16, Ps 51:5, Eccl 8:11, 9:3, Ro1:29, 30, 31,32 Titus 3:3, therefore Solomon writes Pr 4:23-note).

In this section Paul "strings together" a series of OT passage (this technique is called a charaz, literally “stringing pearls” - but this "necklace" is really a noose for all men!) was common at the opening of synagogue homilies and in the Dead Sea Scrolls. Jews and early Christians had Testimonia (quotations from the Old Testament) strung together for certain purposes as proof-texts. Paul may have used one of them or he may have put these passages together himself. In either event, Paul here this catena ("like a chain" = a connected series of related things) to prove his point  "that both Jews and Greeks are all under sin" (Ro 3:9-note)

THE TOTAL DEPRAVITY
OF MANKIND

What we have in this statement and in the following verses is the most explicit description of the total depravity (A vitiated [injured, perverted, spoiled, impaired] state of the heart; wickedness; corruption of moral principles; destitution of holiness or good principles) of mankind in all of Scripture. This does not mean man is as depraved as he could be, but that there is always room for “deprovement” because he is under the power of sin.

Total depravity is one of those "watershed" doctrines, being generally believed by the Calvinists and rejected by the Arminians.

Dr Charles Ryrie offers these thoughts on total depravity...

The scriptural evidence provides the basis for what has been commonly called total depravity. The English word “depravity” means perverted or crooked. It is not used in the translation of the King James Version, but some modern translations do use it to translate adokimos (Ed: word study) in Romans 1:28 (see note). This word (adokimos) means “not standing the test” and gives us a clue as to how to define the concept of depravity. Depravity means that man fails the test of pleasing God. He denotes his unmeritoriousness in God’s sight. This failure is total in that (a) it affects all aspects of man’s being and (b) it affects all people.

Negatively, the concept of total depravity does not mean (a) that every person has exhibited his depravity as thoroughly as he or she could; (b) that sinners do not have a conscience or a “native induction” concerning God (Ed: eg, see Ro 2:14, 15-note); (c) that sinners will indulge in every form of sin; or (d) that depraved people do not perform actions that are good in the sight of others and even in the sight of God (Ed: But see caveat in study of Good Deeds).

Positively, total depravity means (a) that corruption extends to every facet of man’s nature and faculties; and (b) that there is nothing in anyone that can commend him to a righteous God.

Total depravity must always be measured against God’s holiness (Ed: See God's attribute-Holy). Relative goodness exists in people. They can do good works, which are appreciated by others. But nothing that anyone can do will gain salvational merit or favor in the sight of a holy God. (Ryrie, C. C. Basic Theology : A Popular Systemic Guide to Understanding Biblical Truth. Chicago, Ill.: Moody Press)

The Pocket Dictionary of Theological Terms defines total depravity as follows...

Depravity refers both to the damaged relationship between God and humans and to the corruption of human nature such that there is within every human an ongoing tendency toward sin. Total depravity refers to the extent and comprehensiveness of the effects of sin on all humans such that all are unable to do anything to obtain salvation...The term suggests as well that the effects of the Fall extend to every dimension of human existence, so that we dare not trust any ability (such as reason) that we remain capable of exercising in our fallen state. (Grenz, S., Guretzki, D., & Nordling, C. F. Pocket Dictionary of Theological Terms. Downers Grove, Ill.: InterVarsity Press) (Bolding added for emphasis)

Naves has the following entry on Scriptures that speak of the Depravity of Mankind...

Gen. 6:5, 6, 7, 8, 11-13; Gen. 8:21; Deut. 32:10; Job 4:17-19; Job 9:2, 3, 20, 29-31; Job 11:12; Job 14:4; Job 15:14-16; Job 25:4-6; Psa. 5:9; Psa. 14:1, 2, 3 Psa. 53:1, 2, 3. Psa. 51:5; Psa. 58:1, 2, 3, 4, 5; Psa. 94:11; Psa. 130:3; Psa. 143:2; Prov. 10:20; Prov. 20:6, 9; Prov. 21:8; Eccl. 7:20, 29 2Chr. 6:36. Eccl. 8:11; Eccl. 9:3; Isa. 1:5, 6; 42:6, 7; 43:8; 48:8; 51:1; 53:6; 64:6; Je 2:22, 29; 6:7; 13:23; 16:12; 17:9; Ezek. 16:6, 37:1, 2, 3, 36:25, 26; Ho 6:7; 14:9; Mic. 7:2-3, 4; Mt. 7:17; 12:34, 35; 15:19 Mk 7:21-23. Lk 1:79; Jn 1:10, 11; 3:19; 8:23; 14:17; Acts 8:23; Ro 2:1; Ro 3:9-19, 23; Ro 5:6, 12-14; Ro 6:6, 19, 20; Ro 7:5, 11, 13, 14, 15, 18, 19, 20, 21, 23, 25; Ro 8:5, 6, 7, 8, 13; Ro 11:32; 1Co 2:14; 1Co 3:3; 1Co 5:9, 10; 2Co 3:4, 5; 2Co 5:14; Ga 3:10, 11, 22; Ga 5:17, 19, 20, 21; Eph. 2:1-2, 3, 12; Eph. 4:17-18, 19, 22; 5:8, 14; Col 1:13, 21; Col 2:13; Col 3:5, 7; 2Ti 2:26; Titus 3:3; Jas. 3:2; 4:5; 1 Pet. 1:18; 1Pe 2:9, 25; 1Jn 1:8, 10; 2:16; 3:10; 5:19; Re 3:17

As an illustration of all men's depravity (all born with the "genetic defect" called sin) by thinking of the color of sin as blue. If that were true, then every aspect of every one of us would be some shade of blue! The Latin precursor of our word radical is the word radix, which means “root.” We are all infected with this radical corruption called sin as Paul explains later writing...

Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned (see note Romans 5:12).

We are morally ruined down to our very roots. Jesus said the fruit is corrupt because the tree is radically corrupt (cf Mt 7:15, 16, 17, 18, 19, 20 - see notes 7:15-16, 17-20).

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MAN'S TOTAL DEPRAVITY ILLUSTRATED - In November, 1971,  in a Toronto park a duck named "Ringo" made headlines in the local newspaper for several days. The duck who made her home at the park lake, one day accidentally poked her bill through the ring of a pull tab from a pop can and was not able to extricate herself. She was unable to eat and starvation was certain. When her plight was noticed by some park visitors, she became something of a celebrity. Park personnel and animal experts tried numerous ways to catch Ringo so she could be helped. They even called in a champion duck caller. People tried luring her with food. The frightened Ringo mistook all the efforts to help her as threats. What happened to poor Ringo? She disappeared before anyone could come to her rescue. Every man ever born is just like Ringo, trapped in sin and destined to die, temporally and eternally. And just like Ringo sinful man sees the call of the gospel as a threat to his life-style rather than as the eternal blessing it is. And thus they make every effort to escape the only "news" that can ever provide rescue.

THERE IS NONE RIGHTEOUS : hoti ouk estin (3SPAI) dikaios: (Ps 14:1, 2, 3; 53:1, 2, 3) (23; Job 14:4; 15:14,16; 25:4; Jer 17:9; Mt 15:19; Mk 7:21,22; Mk 10:18; 1Cor 6:9,10; Gal 5:19, 20, 21; Eph 2:1, 2, 3; 5:3-6; Col 3:5, 6, 7, 8, 9; 1Ti 1:9,10; 2Ti 3:2, 3, 4, 5; Titus 3:3; 1Jn 1:8-10; Rev 21:8; 22:15)

This sentence is like a summary for the following discourse.

None (3756) (ou) which expresses direct and full negation, independently and absolutely, and hence, objectively. It is important to note that nine times in this section in Romans 3 Paul uses the words such as none and all to show the universality of human sin and rebellion.

Newell writes that...

First, then, as a Judge God describes man's condition: Verse 10: To begin with, There is none righteous before God, no, not one (Ps 14:1; 53:1; Job 9:2; Ecc 7:20). No human being has in himself ever been righteous. Even Adam was not righteous: he was innocent-not knowing good and evil. Let us put far from our minds the fond falsehoods of philosophy, science, and human "religions, " that there have been men of our race who have attained to a standing before God in righteousness. (Romans 3: Sermons)

Righteous (1342) (dikaios from dike = right, just) defines that which is in accordance with high standards of rectitude (the quality of being straight).

Noah Webster has the following definition of rectitude...

In morality, rightness of principle or practice; uprightness of mind; exact conformity to truth, or to the rules prescribed for moral conduct, either by divine or human laws. Rectitude of mind is the disposition to act in conformity to any known standard of right, truth or justice; rectitude of conduct is the actual conformity to such standard. Perfect rectitude belongs only to the Supreme Being. The more nearly the rectitude of men approaches to the standard of the divine law, the more exalted arid dignified is their character. Want of rectitude is not only sinful, but debasing. (Webster, Noah. An American Dictionary of the English Language. 1828)

Dikaios defines that which is in right relation to another and so in reference to persons defines the one who is morally and ethically righteous, upright or just. From a legal viewpoint dikaios refers to one who is law-abiding (doing all that law or justice requires), honest and good in behavior and from a religious viewpoint one who is rightly related to God. In simple terms this trait describes being in accordance with what God requires. The righteous man does what he ought. He is the person who conforms to the standard, will or character of God.

Dikaios is used in its basic sense of “conforming to a norm” and that norm is the Law of God, in whatever form it is available and relevant to man. The Jews had the written Law. The Gentiles on the other hand

show the work of the Law written in their hearts, their conscience bearing witness, and their thoughts alternately accusing or else defending them. (see note Ro 2:15)

This text says that absolutely not a single individual has ever conformed to this norm, but that instead everyone has broken God’s Law and thus ultimately everyone has sinned (Ro 3:23-note). There is not a single man or woman born who is born "right" with God. Sin has affected every aspect of every man - intellect, emotions, volition, etc. Everything and everyone (= total) is  tainted with sin. This state as discussed above is referred to as total depravity. Don't misunderstand. The idea is not that every person is as bad as they could be, but that every part of their being is contaminated with sin and consequently there is nothing anyone can do to commend themselves to a holy God.

Solomon concurs with Paul's indictment writing that

Indeed, there is not a righteous man on earth who continually does good and who never sins. (Eccl 7:20)

No one is righteous in an absolute sense, in the sense of sinless perfection, which is the only way man can be accepted by God (see comment below). Paul is painting a very clear picture that every individual ever born has need for the gift of God's righteousness, which is revealed and offered in the gospel,

for in it (the good news) the righteousness of God is revealed from faith to faith. (see note Ro 1:17).

Righteousness is a major theme of the book of Romans, appearing in one form or another more than thirty times. Other terms from the same Greek root are usually translated “justified,” “justification,” or the like. Together they are used more than 60 times in the book of Romans.

It is not surprising, therefore, that the first charge Paul makes in the indictment is that of mankind’s unrighteousness.  Thus righteousness is not only the key word in Romans, it is also a key criterion by which sin is judged.

As noted above, Paul is using the term righteous in its most basic sense of being right before God, of being as God created man to be, sinless before the "Fall" in the Garden of Eden.

You may be reasoning that sure I do some bad things but the good things I do outweigh the bad. Paul would doubtless agree that people can do many things that appear to be morally right. Even the most vile person may occasionally do something commendable. In the present indictment however, Paul is not speaking of specific "righteous" acts or even general patterns of behavior, but of one’s general character. Paul's point is that there is not a single person who has ever lived, apart from the sinless God-Man , Jesus Christ, Whose innermost being could be characterized as righteous by God’s standard, which is perfection.

God’s standard of righteousness for men is the righteousness that He Himself possesses, which was manifest in Christ. This is the idea Jesus sought to convey to His Jewish audience on the "Sermon on the Mount" declaring that

Therefore you are to be perfect (attained to  moral maturity, reaching this goal, the standard being our Father), as your heavenly Father is perfect.” (see note Matthew 5:48, cp Mt 5:45-note)

The righteousness demanded of citizens of the kingdom of God cannot be attained by merit, but must be given by God. In other words, a person who is not as good as God is not acceptable to God. As Paul makes clear later in Romans, and as the New Testament teaches throughout, men can become perfectly righteous, when the righteousness of Christ is imputed (to set to the account of) or accounted to them (placed on their spiritual account so to speak).

The very truth that makes the Gospel the good news is that God has provided a way for men to become perfect, divinely perfect, perfectly righteous in Christ. This perfection is attainable only by God’s grace and a personal response of placing one's faith in His Son, Jesus Christ. Paul writes

But God, being rich in mercy, because of His great love with which He loved us, even when we were dead in our transgressions, made us alive together with Christ (by grace you have been saved)...For by grace you have been saved through faith; and that not of yourselves, it is the gift of God not as a result of works, that no one should boast." (Eph 2:4,5-see notes ; Eph 2:8, 9 - note)

Spurgeon commenting on Ps 53:1 which parallels Ps 14:1 (quoted by Paul here in Ro 3:12) adds that

Without a single exception people have forgotten the right way. This accusation twice made in the psalm (Ps 53), and repeated by the apostle Paul, is an indictment most solemn and sweeping, but He who makes it knows what is in man.

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