God saw fit that this passage was note and addressed in the NT . Seems this speaks clearly to the sinful nature of man..
Psa 14:2 The LORD looked down from heaven upon the children of men, to see if there were any that did understand, and seek God.
Psa 14:3 They are all gone aside, they are all together become filthy: there is none that doeth good, no, not one.
Notice the Psalmists says that "they had all become filthy." Not that God or the fall had made them that way.
Rom 3:10 As it is written, There is none righteous, no, not one:
Rom 3:11 There is none that understandeth, there is none that seeketh after God.
Rom 3:12 They are all gone out of the way, they are together become unprofitable; there is none that doeth good, no, not one.
Rom 3:13 Their throat is an open sepulchre; with their tongues they have used deceit; the poison of asps is under their lips:
Rom 3:14 Whose mouth is full of cursing and bitterness:
Rom 3:15 Their feet are swift to shed blood:
Rom 3:16 Destruction and misery are in their ways:
Rom 3:17 And the way of peace have they not known:
Rom 3:18 There is no fear of God before their eyes.
However, Paul does not say that man is unable to seek God. He said in Romans 1, that it was man's choice to turn away from God. That is why those who did/do that are without excuse.
Rom 1:20 For the invisible things of him from the creation of the world are clearly seen,
being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse:
Rom 1:21 Because that,
when they knew God, they glorified him not as God, neither were thankful; but became vain in their imaginations, and their foolish heart was darkened.
Noah, Abraham, etc. were not these kind of men.
John the Baptist's parents were found to be righteous. So he can't be speaking about all individuals.
Deu 4:28 And there ye shall serve gods, the work of men's hands, wood and stone, which neither see, nor hear, nor eat, nor smell.
Deu 4:29 But if from thence thou shalt seek the LORD thy God, thou shalt find him, if thou seek him with all thy heart and with all thy soul.
Mat 7:7 Ask, and it shall be given you; seek, and ye shall find; knock, and it shall be opened unto you:
Mat 7:8 For every one that asketh receiveth; and he that seeketh findeth; and to him that knocketh it shall be opened.
Mat 7:9 Or what man is there of you, whom if his son ask bread, will he give him a stone?
These scriptures say to me that God did not create man so depraved that he cannot seek God and that the fall of man did not leave him in this total depravity that is taught in the doctrine of TULIP.