When the iMessages account will not Login
At times for a small number of people the iMessages account stop logging in.
Mostly it happens at Updates and Upgrade.
The people it effects are random in that is can be any Update or Upgrade on any model of Mac with no apparent lead to any combo of software installed.
Back at the OS X 10.8.2 update Messages was updated to version 7.0.1 and since then has needed to see the Serial Number of the Mac as a security feature.
It confirms that the Mac logging in each time you turn it and on launch Messages the iMessages account is from your computer.
You can create the above message if you Migrate a Mac User Account from another computer if you include th Keychain as the IDS: Apple ID-Auth Token references the Serial number as well as the ID and Password.
As you have found when this issue happens it is device specific.
As well as creating the issue when Migrating it can also seem to happen to people randomly at Updates and Upgrades.
Apple are still working on this. (They will not admit there is a problem until they find the fix - even though it has been occurring since Yosemite in it's current form)
Things to do before phoning Apple.
1) NVRAM reset How to reset NVRAM on your Mac - Apple Support. Then test Messages
2) Safe Boot then retest Messages
These two provide some basic Maintenance by clearing caches and resetting some stored Memory items that might be effecting things.
Try Messages in between each one.
3) Check the Serial Number appears in the About this Mac item in the Apple Icon Menu top left.
If it is Missing you will need to Visit an Apple Store to have it "flashed" back to the Mother/Logic board.
If you have had this Replaced recently return to that engineer to finish his or her job
4) Try the Apple ID in another Mac user Account. Create one or Enable the Guest option in System Preferences > Users and Groups.
5) Try a different Apple ID whilst in the test account
6) Try the different Apple ID in the normal Mac User Account.
7) Check the System Information (Apple Menu again but hold down the ALT key and select the first item). Go to Hardware > Network > Locations
This should have one item that has the en0 number. IF you have Ethernet abilities it should be that option. If you don't the WiFi one should become the en0 numbered item.
NOTE 7) has only been posted by one person saying it was a fix from Apple (there is more about what to delete if there is no en0) But no-one I have posted the info to has had an issue with a missing en0 item.
If none of these get Messages to do the iMessages login and it appears to be centred on the use of your Apple ID then it is most likely server end.
At this point you need to phone Apple Support (Apple Care) and say you have an Apple ID issue. (Free to fix)
Level responders do not tend to know about this as they tend to focus on Software and Hardware issues and are somewhat Script led.
You will need to ask to speak to someone higher.
Explain the steps you have done yourself.
Ask if they can look at the server and confirm that your ID, when used from the Mac, is being blocked. (If they can't look ask to speak to someone that can).
Ask for it to be reset.
It is likely that they will contact the engineers as they are the only ones who can reset this now.
You will get a time frame (24 hours to 5 days have been posted back here).
It is fair to say you may be asked to gather data, try other things ( A Reinstall WILL NOT work) to try and fix this as Apple look for answers.
How much time and effort you are will to put into this is up to you.
Hope this helps.
8:58 pm Saturday; February 25, 2017
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 10.x and an iPad (2)