If it doesn't let you add an email login, it means the account does already have one and you must have forgotten it. You would then need to use the tools on the Forgotten login support page to help retrieve the login. There are several pathways on that page, depending how you answer the questions. Try answering them in different ways to see if you can get the login.
Sorry for banging on about the login when you really need to get the registered email sorted (as per what Chief Elf said). But the thing is, you cannot make changes or reset the registered email until you can identify the account correctly. So this issue starts by correctly identifying the login for the account and then you can work on the registered email problem.