Short answer - You are probably out of luck.
The links that go to Change Password and Forgot Password don't work, and haven't for a loooonnnnnnnnnggggggg time. Months. Several. So... you are probably out of luck, unless you can somehow retrieve the e-mail, or remember it somehow.
Forget about trying to contact Cartoon Network through the feedback links, they don't work, for even longer than the password links. Not to mention that Cartoon Network never replies to those anyway.
As far as not being able to create a new account - I'd try on several computers. It may be that it's just not working on the one(s) you are trying to use.
My other guess is that because the game is officially "over" they may not be allowing any new accounts to be made, but I really doubt that, but I wouldn't put it passed them either. I really think they would still allow new accounts to be made, but the wordage I'm seeing is "you can still finish" which speaks to those that have already started, not those that haven't yet.
So I don't know. Hopefully, you can remember your account information. If not, hopefully you'll still be able to create a new account. Like I said, keep trying and try on multiple computers. Have a friend even try to make an account for you and tell you what the log in info is, then try to log in at school (although, I do not condone playing online at school, that's not what you're there for, but I understand there is free time if all your work is done. Sorry, "mom moment"). lol
Anyway, I really hope that helps. If not, sorry!
~Vicks
P.S. No loggin issues for me, but then I know my log in information. But I can log in just fine.