If your account has been permanently banned, then all your accounts are too (conceptually). Technically, you should move this thread to Meta, as it’s the only board you are allowed to post in in order to appeal or try to get a more thorough explanation. A ban applied to a person (and therefore to all past, present or future accounts created by that person).

Is your prior account this one?:
https://bitcointalk.org/index.php?action=profile;u=1260405