First, it's really not helpful to throw out bombs such as, "So, which do you believe, the scriptures or the doctrines of men?" Of course I believe the Scriptures. I just disagree with you on the interpretation of Scripture. I'm charitable enough to extend you the courtesy of your view even if I disagree with it.
As far as John 1, look at the following verse:
John 1:13 who were born, not of blood nor of the will of the flesh nor of the will of man, but of God.
Now, I can say, "LOOK! They were not born again of their own will but of the will of God!"
All this to prove a point. The both of us - you and me - have a theological presupposition. Before we even open the pages of Scripture we're approaching it with a formed opinion about how Scripture operates. That is why the both of us can look at the exact same passage and come away from it with two opposite interpretations. So, when we both have our cannons pointed at each other, accusing the other of following doctrines of men, how does that display grace and Christian charity?
Verse 13 starts with the word "which" which points back to the "them" in verse 12. Verse 12 says to "them" that received Jesus, to "them" God gave the power to become the sons of God, even "them" which believe on his name. Verse 13 is simply explaining what "becoming" a son of God is, it is being born again by God. A man cannot will himself to be born again, this operation can only be performed by God, nevertheless, God only regenerates those that believe.
Ephesians 2 does not even mention faith until verse 8. It says absolutely nothing about a man being unable to believe. Spiritual death means separation from God in sins, not inability. Adam and Eve were spiritually dead when they sinned, yet they were able to respond positively to God and come to him when he called.
As far as 1 Cor 2:14, if you go back to verse 12 you will see these persons have already believed.
1 Cor 2:12 Now we have received, not the spirit of the world, but the spirit which is of God;
that we might know the things that are freely given to us of God.
Does this verse say we have received the Spirit that we might "believe"? No. It says we have received the Spirit that we might know the "things" that are freely given us.
Now go to Galatians 3;
Gal 3:2 This only would I learn of you, Received ye the Spirit by the works of the law, or by the hearing of faith?
This question demands the answer that these Galatians received the Spirit by believing. Believing occurs first, receiving the Spirit comes next. Ephesians 1:13 also says this.
So, these persons in 1 Corinthians 2:12 had already received the Spirit, so they had already believed. Now, upon receiving the Spirit, now they are able to know these "things" of God.
But that is not all, this is also shown in Proverbs.
Prov 1:23 Turn you at my reproof: behold, I will pour out my spirit unto you, I will make known my words unto you.
This verse shows we #1 TURN. We repent at God's reproof and turn to him in trust. Then this verse says #2 God will pour out his Spirit unto us. Receiving the Spirit follows turning to God in repentance and faith.
But now notice what happens next, because it directly relates to 1 Cor 2:12 and 14. Now this verse says #3 I will make my words known unto you.
So, we repent at God's reproof, we next receive the Spirit, and third we are given understanding to know these "deep things of God".
1 Cor 2:14 does not say a man is unable to believe the gospel, it says an unregenerate man cannot understand these "deep things" of the Spirit.
Show me any verse that says all men do not have the ability to believe. You will not be able to show it, because it doesn't exist. It is a purely man-made doctrine not supported by scripture.