Q: Apple id not working after 10.11.6

Hello muyaszed,

Thank you for using the Apple Support Communities. I know having an issue with your Apple ID after updating your Mac is not what you expect. If I understand correctly, you are unable to put in your Apple ID info on your Mac, even though your Apple ID is work on your other devices. I recently had an issue similar to yours, and here are a couple of steps that can help resolve your issue:

1. First, I suggest signing out of your Apple ID in any app you're having this Apple ID issue with. This article has a nice list and step by step directions for each app that could use Apple ID:

What to do after you change your Apple ID email address or password

2. Next, restart your Mac and then try signing into your Apple ID again in an app, like FaceTime or iCloud in System Preferences.

How to turn on or turn off your Mac

3. If you're still having an issue at this point, use Safe Mode to start up your Mac so that it performs certain checks, delete system cache files, verifies your startup disk, and attempts to repair directory issues if needed. Then test your Apple ID issue again.

Try safe mode if your Mac doesn't finish starting up
Limited graphics performance in OS X recovery or safe mode

Cheers!