Let's look at your question:Martin, not trying to insult anyone just pointing out what I have seen on these sites. Sorry that you think I have a holier-than-thou attitude that's not my intent.
You almost got the whole thing right. Man has a free will and that is why he does what he does and because of that the judgement is deserved. My question for you is when are sinners born again before or after they believe?
And in regard to 'irresistible reprobation,' why don't you look at the theology that you hold to. The logical outcome of calvinist views lead to this result. Your a logical man so be honest with yourself and think it through.
...when are sinners born again before or after they believe?
The term "born again" is found in John 3. There Jesus is having a dialog with Nicodemus. Jesus states:
Jesus answered him, “Truly, truly, I say to you, unless one is born again he cannot see the kingdom of God.” Nicodemus said to him, “How can a man be born when he is old? Can he enter a second time into his mother’s womb and be born?” Jesus answered, “Truly, truly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God. That which is born of the flesh is flesh, and that which is born of the Spirit is spirit. Do not marvel that I said to you, ‘You must be born again.’ The wind blows where it wishes, and you hear its sound, but you do not know where it comes from or where it goes. So it is with everyone who is born of the Spirit.” Nicodemus said to him, “How can these things be?”
Based on Jesus dialog, that new birth has nothing to do with human will. It has everything to do with God making someone new.
Let's compare with what God tells us through the Apostle Paul.
For while we were still weak, at the right time Christ died for the ungodly. For one will scarcely die for a righteous person—though perhaps for a good person one would dare even to die— but God shows his love for us in that while we were still sinners, Christ died for us.Since, therefore, we have now been justified by his blood, much more shall we be saved by him from the wrath of God. For if while we were enemies we were reconciled to God by the death of his Son, much more, now that we are reconciled, shall we be saved by his life. More than that, we also rejoice in God through our Lord Jesus Christ, through whom we have now received reconciliation.
~ Romans 5:6-11
For if we have been united with him in a death like his, we shall certainly be united with him in a resurrection like his. We know that our old self was crucified with him in order that the body of sin might be brought to nothing, so that we would no longer be enslaved to sin. For one who has died has been set free from sin. Now if we have died with Christ, we believe that we will also live with him. We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him. For the death he died he died to sin, once for all, but the life he lives he lives to God. So you also must consider yourselves dead to sin and alive to God in Christ Jesus.
~ Romans 6:5-11
Or do you not know, brothers—for I am speaking to those who know the law—that the law is binding on a person only as long as he lives? For a married woman is bound by law to her husband while he lives, but if her husband dies she is released from the law of marriage. Accordingly, she will be called an adulteress if she lives with another man while her husband is alive. But if her husband dies, she is free from that law, and if she marries another man she is not an adulteress. Likewise, my brothers, you also have died to the law through the body of Christ, so that you may belong to another, to him who has been raised from the dead, in order that we may bear fruit for God. For while we were living in the flesh, our sinful passions, aroused by the law, were at work in our members to bear fruit for death. But now we are released from the law, having died to that which held us captive, so that we serve in the new way of the Spirit and not in the old way of the written code.
~ Romans 7:1-6
The answer to your question then is this:
God does all the work. We die to sin in Christ. We are then raised to new life in Christ (born again). We are justified in this truth...by faith.
Since we are slaves to sin and its wages is death, we cannot believe in that state. We must die with Christ and be made alive (born again) with Christ, before we can believe what God has actually done.
Our redemption is a monergistic act of God, alone. Our sanctification is a synergistic cooperation of our freed will to choose obedience to God rather than obedience to sin. Paul lays this all out in his magnificent apologetic argument in Romans. Paul and Jesus both answer you so that you should not miss this important truth.