Wilt thou forgive that sin where I begun, Which was my sin, though it were done before? (1-2)
If this sin was his before he was even born, then it doesn't seem like he gets much choice in the matter. The concept of Original Sin dooms us humans to accept the fate of sinner before we actually have a chance to earn it. (It'd be kinda like putting a baby in jail for the crimes his parents committed.) The speaker's idea of Original Sin means we don't really have free will; our fate is already decided.
[…] that sin, through which I run, And do run still, though still I do deplore? (3-4)
It seems like the speaker hates sinning but does it anyways. Does he feel like sinning is inevitable because he's human, and thus it's out of his hands? Or is he just too lazy to stop?
And, having done that, thou hast done; I fear no more. (17-18)
As long as God forgives the speaker, he can make it to heaven. It seems like the speaker isn't taking much responsibility for his fate; he's resigned to the role of sinner. It's God who does all the saving. He's saying that man is incapable of saving himself from a dark fate.