Hi,
The Original Poster never answered the question as to whether there was any other sort of error Message.
The Messages app for the iMessage account needs the Apple ID, a password for the Apple ID itself or the 2 Step Verification App Specific one, AND the Serial Number to be able to generate the IDS: AppleID-AuthToken (in the Keychain Password section).
If the Mac User Account is migrated from another computer including the Keychain (and therefore references to the old Serial Number) then the iMessages server will block the apple ID when used from the Mac.
The Serial Number provides a device specific Login.
Also:
apsd: Certificate not yet generated
The Apple Push Service Daemon is used by the Messages app to Send and Receive but is not the cause of any ports not being open.
8:11 pm Saturday; January 28, 2017
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 iMac 2.5Ghz i5 2011 (Sierra)
 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)