Therefore, until God changed your heart, you could not and would not come to Christ. The Lord must open a sinner's heart prior to faith, and in order that the sinner may believe. No, you would not have. Without the prior work of the Holy Spirit, who like the wind, blows when and where He will, you could not and would not have believed. You were going your own way, and would still be going that way today if He had not turned your heart to go His way and to trust in His Son.
Regeneration is the same thing as being born again.
The New Birth is the very first act of God upon your soul in conversion. Everything else flows from it. When God the Holy Spirit regenerates you, giving you a new heart, then you will repent and believe the gospel. When you believe the gospel you are immediately justified and adopted. Paul mentions regeneration and renewing.