Honestly you might be up the creek a bit, as these days I think TNT puts a lot of weight in at the very least being able to identify what email is on your account, even if you don't have access to it. Birthday is definitely good though so if you had any other info you could include especially NC receipts (code redeems or otherwise) you just want to compile everything you could possibly think of (when you adopted/created pets, neofriends, amount in bank acct, items in SDB etc) to hopefully overcome the fact you don't know the email. That being said their system is super backed up right now (even more so than usual) so it's a toss up on when you will get a response. You can always message them on twitter (burner acct is fine) or make a new acct/get a shell to post the ticket number on the highway to help board.Good luck!
