Old iCloud account is the default and I can't change it

I just updated my iPhone to 8.0.2 and now every few minutes I'm prompted to log into my old iCloud account - I can't sign out because I don't remember the password. I can't get my password reset because it's an old work email and the account is unactivated. I tried to reset via security questions but can't get past the date of birth - it tells me the date I enter doesn't match whats on their file. I just want to change the default to my new Apple ID - help?