The reason you can't get on with other accounts is that when you are banned it's an IP ban, not an account ban, so banned people can't make new accounts after they are banned. And asking why you are banned will not result in any answers, the mods on the forum are generally different mods to the ones in game. Some do mod in game but there is only a slight chance that it was one of them that banned you, and they probably don't even remember.
On another note, do you use a mac?