Hi,
Generally speaking a computer cannot be "Backdated" to a version of the OS that it has never used when it has a Newer one from the Start.
i.e. if it came with El Capitan then it cannot run Yosemite or earlier.
As the iMessages server is separate then you can have the issue in only one app.
If you look in System Preferences > iCloud (the most likely place the ID is also used) then there is no setting to Enable it for Messages, or iTunes or the App Store or FaceTime.
This means on one hand that individual Servers can go down and only one app will be affected.
It also means that your ID can be "Suspended" on one server and not on others.
In the case of the iMessages server that is based on each devices unique Login which involves Auth Tokens based on the devices Serial Number.
An over zealous security feature seems to be tripping out some Macs
If...
You have tried a Safe Boot, a NVRAM reset, deleting some of the .plists involved, removing the Auth Token for the IDS: Apple ID info from the Keychain and you still cannot Log in or you appear to be and all Contacts Go Red and say they are "not Registered with iMessages" or each Send get a "Not Delivered" then the account is not Logging in properly.
The ONLY solution is then contact Apple support and say you have a Apple ID issue and join the merry dance (currently they say they don't know of the issue and eventually a Level 2 person will involve the Engineers (they are looking for the trigger) before someone will tell you it takes 24 hours to reset).
I wish you luck at this stage as I have not found any suggestion I have made to people embarking on this is making it any faster.

9:44 pm Friday; December 4, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
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