Do humans possess desires? Can a person who desires his own will instead of God's be changed by God? If he can't be changed why was he made that way? Do you pray for unbelievers?
I think the Bible is clear that we have free will, that we choose whether or not to follow God, and that God will not force a person's will for the good.
And if it is evil in your eyes to serve the Lord, choose this day whom you will serve, whether the gods your fathers served in the region beyond the River, or the gods of the Amorites in whose land you dwell. But as for me and my house, we will serve the Lord. (Joshua 24:15). Kind of a ridiculous choice if there is no true choice. It’s clear you’ll have a choice whether to do God’s will or not.
No temptation has overtaken you that is not common to man. God is faithful, and he will not let you be tempted beyond your ability, but with the temptation he will also provide the way of escape, that you may be able to endure it. (1 Corinthians 10:13). Why provide a way of escape if you can’t escape, if you can’t choose to accept or reject temptation, to choose God’s ways or our own ways?
Let no one say when he is tempted, “I am being tempted by God,” for God cannot be tempted with evil, and he himself tempts no one. But each person is tempted when he is lured and enticed by his own desire. Then desire when it has conceived gives birth to sin, and sin when it is fully grown brings forth death. Do not be deceived, my beloved brothers. (James 1:13-16) We tempt ourselves. We lure ourselves towards evil. God doesn’t do it.
God may perhaps grant them repentance leading to a knowledge of the truth, and they may come to their senses and escape from the snare of the devil, after being captured by him to do his will. (2 Timothy 2:25-26) It is clear here there is an interplay between the person choose and repenting, and coming to their senses, and God granting them repentance.
Therefore I will judge you, O house of Israel, every one according to his ways, declares the Lord God. Repent and turn from all your transgressions, lest iniquity be your ruin. Cast away from you all the transgressions that you have committed, and make yourselves a new heart and a new spirit! Why will you die, O house of Israel? For I have no pleasure in the death of anyone, declares the Lord God; so turn, and live. (Ezekiel 18:30-32) If God did not give free will, what is the point of His pleading?
Seek the Lord while he may be found; call upon him while he is near; let the wicked forsake his way, and the unrighteous man his thoughts; let him return to the Lord, that he may have compassion on him, and to our God, for he will abundantly pardon. (Isaiah 55:6-7) Again, man can return. They can repent. God calling for us to repent makes no sense if there isn't at least some element of free will in there.
I pray for unbelievers. I was one, and I repented. If God saved one such as me, if by His grace I repented, then there is hope for anyone. I don't believe there was any virtue in my act, anymore then if I was dying of thirst in the desert and I drank the water someone offered me. But I admit I struggle with this. There are people I know who are very set in their sin, and short of God forcibly changing their will, I don't see any hope for them. And I don't believe God will forcibly change someone's will. But I pray, because God has commanded it, and because you never really know where a person is. Just a short while ago someone very well could have said there was no hope for me.
C.S. Lewis said, referring to faith and works, that the debate was kind of like arguing about which blade on a pair of scissors was more necessary. I feel that way about the man's will vs. God's will debate. The Scripture is clear that no one can come without God "You did not choose me, but I chose you and appointed you that you should go and bear fruit and that your fruit should abide, so that whatever you ask the Father in my name, he may give it to you. (John 15:16)" It's also clear that action on our part is required. "The Spirit and the Bride say, “Come.” And let the one who hears say, “Come.” And let the one who is thirsty come; let the one who desires take the water of life without price. (Revelation 22:17)" I don't think it's an "either/or" as much as a "both/and".