Every person, ever born, is a sinner. Every person is "dead in trespasses and sins". That means he is spiritually separated from God; In other words, he has no fellowship with God and no knowledge of the things of God because they are "spiritually discerned". Because of this his heart is "desperately wicked".
This is true.
It is that natural state of the fallen, unsaved, destined for hell, heathen, unbeliever. There is "NO fellowship with God and NO knowledge of the things of God." (capital emphasis mine).
"...he is spiritually separated from God" and is already condemned (as John 3 states) because of unbelief.
However, when the Holy Ghost deals with a man's heart, "convincing him of sin, righteousness and judgement", that man, any man has the ABILITY to effectively TRUST or REJECT the Gospel; to "choose life" and live, or choose death and go to Hell. You choose life by admitting that you are on your way to HELL and DESERVE it and at the same time casting your soul at the feet of Jesus. That is NOT of works and there is no human "merit" in it. It's a totally selfish act on your part because YOU don't want to fry in HELL for the rest of eternity. The "total inability" stuff is totally unbiblical and totally untrue.
The "However" is necessary. The work of the Holy Spirit is intricate to salvation and salvation cannot occur outside of that work. It is totally of the Grace of God that the Holy Spirit works, it is not in any human capacity or authority to expect that work, but to acknowledge that work.
The crux of the difference between those who hold a more calvinistic view, and those who hold a more pelagian view is this work of the Scriptures is not accomplished without the Holy Spirit using the Word. The Holy Spirit using the Word of God produces faith (Romans), that ability is not innate and not a "freedom of expression" or "freedom of the will," for there is no life (faith/belief) to be found outside of the Scriptures being used by the Holy Spirit.
Both the arminian and the calvinistic views take a scriptural stand that the Holy Spirit is involved from the start, creating the life.
The Wesley's put in a middle grace, in which some unthoughtful Baptists endorse called prevenient/preceding grace. But such is just not found in the Scriptures either by statement or by example. The Wesley's schooled as Calvinistic thinking, recognizing the truth of that thinking, yet attempted to bridge between Pelagian and Calvinistic thinking by forming some intermediary work of God's grace.
Therefore, both the Arminian and the Calvinistic view hold to total depravity.
What the Pelagian view holds is that from the natural unsaved state, the person may out of their own freedom of expression will themselves into salvation. That the faith is not given by God, but a human attribute in which the human may freely express in acceptance or rejection of salvation.
Therefore, in your last part of the post, you present what is more Pelagian then even Arminian for at least many of the Baptists adopted a Wesley approach of some endowment by God of a grace to lift that person into such a state in which that person could choose.
However, again it must be emphasized that
no such grace exists either in statement of or exampled as a type in the Scriptures. It was and remains a totally human contrivance and a blight against what the Scriptures present as faithful.
What is TRUE?
1) No person has innate ability or even the will to accept, for all have turned and gone their own way.
2) The Holy Spirit awakens the person as Christ said (and you posted).
3) The person that is awaken has been given to the Son by the Father and will be raised to eternal life.
4) Those that are not awakened and not given will spend eternity separated from the Father for such have turned from any light given, even the very evidences of God written on their heart. (Romans 1,2). Such are already condemned (John 3) and have only the desire to avoid and mock the light.
5) That God chooses from among those already condemned and gives to the Son those that are to be saved is not unfair, nor should it not be a concern for the believers to argue. He is the Sovereign and not humankind.
6) Believers are not given permission to ask the Sovereign, "Why," (Romans 9) but are given a mission to deliver the gospel to all the world.