I have no idea what that even means, out of nowhere there was a hack? you don't even know what hack means.
are you saying there was a cheat out of nowhere? on your account? or are you saying you were hacked out of nowhere? meaning your account was compromised, in which case that's a lie since accounts do not get hacked but hijacked after the user is careless with his account credentials.

your old game ban can be for many reasons, all we can tell you is that its permanent and Valve will not remove it or tell you what you did.
you know what you did though, you know very well.