Ironically, when I had an account issue with BF3, their normal support wasn't helping, and I had spent days trying to get the problem fixed. I created a Twitter account and contacted EA Support through there, and the problem was fixed within 24 hours. Kind of weird, but w/e.
And to be honest...kinda your fault for forgetting your password. I mean, it would be the same if you forgot your password for steam. Are you sure you are using the right email? I know that seems like a stupid question, but I don't see how else you wouldn't be getting an email from them.
Any you say that you don't know your Ea ID or password? Isn't your ID your email? You must know one of the two.
This is kind of a side note, but a lot of people hate on origin. I think it's fine. In fact, I've had far more issues with steam not responding and updating games, but I like both pieces of software in the end.