Hi,
We now seem to have two groups of people.
Those without Serial Numbers that have had issues since updating to OS X 10.8.2/Messages verion 7.0.1
Those who have been registered that are now being told they are not.
The Messages app should not spontaneously lose the Apple ID used in the iMessages account. You have to specifically Sign Out of the iMessages account or remove the Apple ID from an iPhone and let the sync process remove it from the Messages app (Normally at the next restart)
It is difficult to work out what is going on in these cases.
Have you been able to add the Apple ID you want to use to the iPhone for Messages ?

9:50 PM Tuesday; January 8, 2013
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously