How is the person that fits your definition of depraved (which is pretty much right on) ever going to "accept" Christ? If one is spiritually dead, and morally corrupt, what would ever motivate him to love God?
The Drawing of the Holy Spirit and yet we see with King Agrippa one who rejected the convicting of the Holy Spirit.
Acts 26:27 King Agrippa, believest thou the prophets? I know that thou believest.
28 Then Agrippa said unto Paul, Almost thou persuadest me to be a Christian.
29 And Paul said, I would to God, that not only thou, but also all that hear me this day, were both almost, and altogether such as I am, except these bonds.
Paul desired that all that heard that day would come to Christ.
Paul said
Romans 10:14 How then shall they call on him in whom they have not believed? and how shall they believe in him of whom they have not heard? and how shall they hear without a preacher?
15 And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach the gospel of peace, and bring glad tidings of good things!
16 But they have not all obeyed the gospel. For Esaias saith, Lord, who hath believed our report?
17 So then faith cometh by hearing, and hearing by the word of God.
Faith comes by hearing and by the word of God as it is preached, and as prechers are sent. All of course is by the plan of God.
Romans 2:1 Therefore thou art inexcusable, O man, whosoever thou art that judgest: for wherein thou judgest another, thou condemnest thyself; for thou that judgest doest the same things.
2 But we are sure that the judgment of God is according to truth against them which commit such things.
3 And thinkest thou this, O man, that judgest them which do such things, and doest the same, that thou shalt escape the judgment of God?
4 Or despisest thou the riches of his goodness and forbearance and longsuffering; not knowing that the goodness of God leadeth thee to repentance?
5 But after thy hardness and impenitent heart treasurest up unto thyself wrath against the day of wrath and revelation of the righteous judgment of God;
6 Who will render to every man according to his deeds:
7 To them who by patient continuance in well doing seek for glory and honour and immortality, eternal life:
8 But unto them that are contentious, and do not obey the truth, but obey unrighteousness, indignation and wrath,
9 Tribulation and anguish, upon every soul of man that doeth evil, of the Jew first, and also of the Gentile;
10 But glory, honour, and peace, to every man that worketh good, to the Jew first, and also to the Gentile:
11 For there is no respect of persons with God.
Notice verse 4 God leads us to repentence.