“Because of the fall we do not have the ability to choose God.”
Don’t tell Jesus: Now after John was arrested, Jesus came into Galilee, proclaiming the gospel of God, and saying, “The time is fulfilled, and the kingdom of God is at hand; repent and believe in the gospel.”
Don’t tell Paul either: “And Paul and Barnabas spoke out boldly, saying, “It was necessary that the word of God be spoken first to you. Since you thrust it aside and judge yourselves unworthy of eternal life, behold, we are turning to the Gentiles.” or “ Let me ask you only this: Did you receive the Spirit by works of the law or by hearing with faith?”
And don’t tell Luke: “At Caesarea there was a man named Cornelius, a centurion of what was known as the Italian Cohort, a devout man who feared God with all his household, gave alms generously to the people, and prayed continually to God. About the ninth hour of the day he saw clearly in a vision an angel of God come in and say to him, “Cornelius.” And he stared at him in terror and said, “What is it, Lord?” And he said to him, “Your prayers and your alms have ascended as a memorial before God.”
The only thing these verses reveal is your misunderstanding of calvinism (the gospel), and the retort is the obvious and the easiest one:
Act_13:48 And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as were ordained to eternal life believed.
At no time have we ever taught that any of those who were ordained to eternal life did not believe, or that they believe against their will. Consider Augustine's explanation, a man who preceded both Calvin and Luther in these teachings, of how God brings a man infallibly to Christ:
"No man comes to me except he whom the Father shall draw. Do not think that you are drawn against your will. The mind is drawn also by love. Nor ought we to be afraid, lest perchance we be censured in regard to this evangelic word of the Holy Scriptures by men who weigh words, but are far removed from things, most of all from divine things; and lest it be said to us, How can I believe with the will if I am drawn? I say it is not enough to be drawn by the will; you are drawn even by delight. What is it to be drawn by delight? Delight yourself in the Lord, and He shall give you the desires of your heart. There is a pleasure of the heart to which that bread of heaven is sweet. Moreover, if it was right in the poet to say, Every man is drawn by his own pleasure, — not necessity, but pleasure; not obligation, but delight—how much more boldly ought we to say that a man is drawn to Christ when he delights in the truth, when he delights in blessedness, delights in righteousness, delights in everlasting life, all which Christ is? Or is it the case that, while the senses of the body have their pleasures, the mind is left without pleasures of its own? If the mind has no pleasures of its own, how is it said, The sons of men shall trust under the cover of Your wings: they shall be well satisfied with the fullness of Your house; and You shall give them drink from the river of Your pleasure. For with You is the fountain of life; and in Your light shall we see light? Give me a man that loves, and he feels what I say. Give me one that longs, one that hungers, one that is travelling in this wilderness, and thirsting and panting after the fountain of his eternal home; give such, and he knows what I say. But if I speak to the cold and indifferent, he knows not what I say. Such were those who murmured among themselves. He whom the Father shall draw, says He, comes unto me." (Augustine, Tractate 26)
All men who receive it from heaven to believe, therefore, do not convert against their will, but are given a new heart of flesh to see and to hear the things of God (Deu 29:4), and once equipped are drawn by the delight of the Gospel revealed to them, so that all who believe are willing believers. And all those who are damned are also willing infidels, happily sinning against God.
The verses I presented from John prove, beyond any doubt, that it is indeed the grace of God, and not man's willing or running, which brings him infallibly to salvation and never lets him go (Rom 9:16). I have never seen any individual who claimed otherwise really take the time to tackle or acknowledge the plain meaning of these verses, which declare, without blushing, that the reason for those Jews' disbelief was in God not giving it to them to believe, and not for any other reason.
Submit to God, not to your own understanding. Holding on to the false premise that it man who gives himself to God, and not God who takes the man, does not save you from the things you wish to avoid. It is a fact that not everyone has heard the Gospel, and many millions, including those Jews as mentioned by Christ, have never been "given" anything by the Father to believe. There are out there, right now, even in American cities, people who will never hear the Gospel and will never have any sort of chance for salvation. They will die in ignorance, without the "chance" you all deem so important to justify God. How do you save yourself from the charge of "unfairness" then, when God does not give an equal chance to all the world to be saved? But the true answer to these problems is not to rob from God His sovereignty in salvation, but rather it is to submit to the scripture:
"As it is written, Jacob have I loved, but Esau have I hated. What shall we say then? Is there unrighteousness with God? God forbid. For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion. So then it is not of him that willeth, nor of him that runneth, but of God that sheweth mercy." (Rom 9:13-16)
And again,
"Thou wilt say then unto me, Why doth he yet find fault? For who hath resisted his will? Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus?" (Rom 9:19-20)
This is hard medicine, but it is the best medicine.
It is God's will that all men believe and come to repentance. Scripture says it in so many words.
This is true, but we must not confuse the prescriptive will of God with His secret decree, or, in other words, His will that all should repent and be saved, with His will to save and cause men to repent. On the one hand, He desires men to be saved, but, on the other hand, there are those whom He will give His mercy to, and those whom He will not, according to His own pleasure.
The scripture only teaches regarding man's will two things. That we will to sin, and that, abundantly, and cannot, without the Holy Spirit, do anything different, for none "seek or understand" God (Rom 3). We are voluntary slaves.
Secondly, the scripture teaches that whomever Christ sets free, they are free indeed, and none whom God begins a work in ever fail to have it completed. And all those who do not believe are specifically told that they were not "given" it by the Father to believe, and not because of any foreknowledge of rejection or faithlessness on their part.
These facts knock down any role in man's willing and running in his salvation, but give all the glory to God, who sees a depraved world and chooses for Himself His own people and does not fail to bring them happily, and willingly, into His arms.