How can you reset your PlayStation Network account's password if you don't know the password or the date of birth you put in?

You can't really...because if people could do that, what's to stop them resetting the passWord on anyone else's account. There are safeguards in place to try to ensure only the account owner can change the passWord, and part of that safeguard is that the account holder knows the details the account was registered with.

Try contacting Sony, if you think you've got enough other info to prove the account is yours.