Hi,
http://www.apple.com/support/systemstatus/ report and iCloud issue 12 hours ago.
As new iMessages user it may not have been able to confirm your ID. I say "may not" as the iMessages are separate apart from checking with the Apple ID servers that the info is correct.
If you go to the Apple Icon Menu top left and About this Mac and then click on the line that tells you the OS it should eventually (at the second click) show you the Serial Number of the Mac.
If you are using Yosemite or El Capitan the About this Mac pane shows it in the Overview tab.
If the Serial Number is missing then iMessages and FaceTime will not be able to Login.
You will have to visit an Apple Store to have it corrected. (I have not heard of anyone being charged for this).
It normally happens if the Mother/logic board has been replaced during a Repair or Refurbishment and someone forgot to "flash" the number back to the board.

7:57 pm Monday; May 9, 2016
iMac 2.5Ghz i5 2011 (El Capitan)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone and an iPad (2)