Q: I can't log off iCloud, I accidentally deleted my email address.

Hello,

So recently people have been telling me that my email address was unprofessional, so I finally made a new one. I changed my Apple ID's primary email to the new email address. On other things, I tried resolving something with Google+, changing the primary email to my new email address. It said I had to delete the previous email address, so I did. That old email address doesn't exist anymore.

But then I remembered that I had forgotten to log out of iCloud on my MacBook. Even though I changed my Apple ID's address, it hadn't switched yet on the iCloud window in System Preferences. I tried to log off, and it was disabling every function one by one (as usual), but when it got to iCloud Keychain, it said I needed to disable it manually. But for some reason, it seems to be blocked.

Above, it asks me to type in my ID's password to disable it, but since that email address does't exist anymore, it says it's incorrect. I already tried it many times, so it tells me my account has been disabled and that I need to reset my password.

Okay, I go to reset it, and first it asks me for my Apple ID, so I type in my old email address, and then it gives me the option to send an email or answer security questions. I choose the questions because the email would never be received. The when it asks me my birth date, it says it's incorrect. I have already verified it was correct, so now I don't know what to do.

Is there a way to disable iCloud completely or make it log off by itself? Because I have tried everything and it won't work because it keeps asking me things about a now inexistent email address. Please help.