I cannot sign out of iCloud in my Mac (os Sierra) after changing my Apple ID and password.
I recently changed my Apple ID and password and I'm trying to update all Apple services in my 3 devices. The iPhone and iPad iCloud settings seemed to have already updated automatically to the new account. However, my Mac is not allowing me to sign out of the old iCloud account ( old Apple ID email). It keeps asking me to enter the password for the old iCloud account (which no longer exists) in order to sign out. Apparently it's something to do with "Find my Mac" being activated in the iCloud account but I cannot deactivate it without the password for the old account.
I've tried to remove my Mac from the list of devices using "Find my Phone" in iCloud.com (but the moment the Mac is back online it reappears).
I 've also tried to enter old and new passwords to sign out of iCloud in Mac but i get a message saying the account doesn't exist and so, I'm stuck in that loop.
Any ideas on how to resolve it? I'm reluctant to change my Apple ID back to the old one in case it creates other issues with my other devices and then I'll be trully stuck...
Thank you very much
MacBook Air, macOS Sierra (10.12.2)