Been looking for a solution for the 'Your device or computer could not be verified' message. I found it.
Here's a little background: Because wifi and bluetooth suddenly stopped working it turned it in for repair. It was almost two years old, so it was still under 'warranty'. They ended up replacing the Logic Board. When I got it back I couldn't login to the computer with the password the store had chosen (1234) and written down to the technicians.
I ended up resetting the password of the account (https://coolestguidesontheplanet.com/reset-forgotten-admin-password-mac-osx/).
But trying to setup facetime and message + login into app store failed. One of the messages I got was the 'Your device or computer could not be verified'.
I upgraded to El Capitain, still with no luck.
I tried some of the suggestions made here, with no luck.
Solution: Then I ended up clean install El Capitain – but at the same time I logged into my iCloud from Safari from my MBP and then removed my Macbook Air from the list of devices. When I entered my iCloud settings during the install – everything worked fine... message, facetime, settings > iCloud, app store.
I don't think the clean install has anything to do with it. Removing my Macbook Air from iCloud from my MBP, then adding it again from my MPA – is probably what did it.
Hard rebirth...