Whoa, back the truck up a bit.
Forgiveness IS to remove the punishment due to a transgressor - HOWEVER - God did not just decide to not punish transgressors for their sins - that would be unjust according to His Law.
Someone had to take that punishment - and did - CHRIST:
2 And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world. (from 1 Jn. 2)
God's justice was satisfied with Christ's Sacrifice. Payment has already been "exacted", and Hebrews 9 tells us this:
28 so Christ, having been offered once to bear the sins of many, will appear a second time, not to deal with sin but to save those who are eagerly waiting for him.
Sin was already dealt with completely at the Cross. When Jesus comes back, He will simply sort those who believe from those who don't believe - the only unpardonable sin is the sin of unbelief.
Forgiveness AND righteousness AND New Life are gifts entered into by faith - believing in what Jesus did and what that means.
Repentance is a part of that, but not in the way you might think (turning from sin). Repeating from an earlier post in this thread:
Repenting is often mis-defined as 'turning from sin'. Let's look at the Biblical definition for repentance:
Repent - Strong's G3340 - metanoeō
[*=1]to change one's mind, i.e. to repent
[*=1]to change one's mind for better, heartily to amend with abhorrence of one's past sins
Repentance - Strong's G3341 - metanoia
[*=1]a change of mind, as it appears to one who repents, of a purpose he has formed or of something he has done
One might change their mind about Christ and who He really is, or one may have a basic religious understanding of Who Christ is but never understood just what Christ accomplished with His Work and High Priesthood on their behalf. In that case, one would need to change their mind about Christ and His Work and then believe - put their faith in - Christ.
Turning from sin will eventually be a result of believing and becoming a New Creation in Christ, but it is not a requirement. Saying that one must turn from sin to receive salvation is akin to requiring one to become clean before taking a bath - it makes no sense, and asks the spiritually dead to accomplish what only spiritual life can do for them.
Now about that changing of one's mind.
Therefore, I urge you, brothers and sisters, in view of God’s mercy, to offer your bodies as a living sacrifice, holy and pleasing to God—this is your true and proper worship. 2 Do not conform to the pattern of this world, but be transformed by the renewing of your mind. Then you will be able to test and approve what God’s will is—his good, pleasing and perfect will. (from Rom. 12)
How does this happen? By sheer willpower?
And who is that written to?
Believers or unbelievers?
Repentance, Biblically defined, is a part of salvation (the changing of one's mind to believing rightly about Christ and His Work) and faith is how we enter into His New Covenant.
Repentance is also an ongoing process in the believer, as we are transformed by the renewing of our minds. As we learn to believe rightly about Who Jesus is, what He did, what that accomplished, and who we as believers are in Him, right behavior follows. It's actually Fruit. As we align with and abide in and rest in Christ, being led by His Spirit, Fruit happens (Gal. 5) \o/.
For those who are willing, the following communicates the above and other concepts really well:
-JGIG