All sites have very strict rules regarding such issues, since I'm afraid there some people trying to cheat, to create multiple accounts, etc...
So you must convince them politely that it's not you. From my experience, the best thing to do when there's an issue with an agency is to be as detailed as possible, tell them (again) that you really regret deleting your account...
Don't stop at their first negative answer, you may get a different answer if you contact them again;
but don't try to open a new account before clearing this issue; hoping they don't find out is useless: they have your name, address, id and will find out sooner or later and you'll even risk passing for unsincere even if it's not your case