How to not be recognized on banned forum?

When I first got my computer and internet connection I joined a major/large worldwide discussion forum. As a newbie I was harassed in a way that didn't violate the rules. But I replied back harshly instead of ignoring. That got me permanently suspended from the site. I tried to create a new account, but can't. Then I went to the public library and successfully created an account. When I log in from my computer at home I get that account closed by the end of the day.

All I can do is read the discussion threads.

I assume it is my I.P. address that is being recognized. Or is it the cookies in my home computer? (I notice some sites say they will put cookies in the computer to better my usage).

So, the time has come for me to get a new internet provider. Next week I will have a new I.P. address. Will I be able to successfully create an account with a new I.P. address? Or will I have to clear out my computer's cookie memory to keep from recognizing me as a banned member?