Wait a month or two and ask support@thinkingape.com to appeal your perma-silence. Be honest or else your not getting un-silenced.
There is a reason the third silence is called permanent, even though that is not always the case. You were given two warnings in the form of 24 hrs silences. If you can't get an understanding of the rules by then, you deserve the permanent silence. However, although I believe the third silence should be permanent, there is a way to reverse it. After a month or two email support@athinkingape.com. Explain your situation (the reasons for your silences, that you've gone without chat for all this time, and that you regret what you've done and that you won't break the rules again). Most likely you'll be unsilenced. Of course, breaking rules in forums in the mean time won't help your case. And do be honest with support. If you manage to get unsilenced, then you should take care not to break the rules again. Because if you're silenced again you're back to permanent and chances of being unsilenced again are extremely slim.