File your appeal right here in Meta, and state exactly what account was banned. 

Do members get permabanned for PM spamming?  I thought only plagiarism was grounds for that, though I confess I have no idea what the penalty is for spamming.  I'm thinking that if the account wasn't banned for plagiarism, OP might have a shot at having it restored, but I'm not a moderator and I'm definitely not Theymos.

If you want any chance at reinstatement, OP, whatever you do don't create a new account and start using it to post outside of your ban appeal thread in Meta.  Ban evasion will get you a permaban on top of your permaban.