Hi,
When the Apple ID is inactive (removed/signed out) in Messages on the iPhone it is only the iPhone Number that is left in in the Send and Receive options ?
Also in this state can you iMessages from the iPhone to the Apple ID (i.e only the Mac should be able to see the iMessage) ?
In addition can the Mac then iMessage back to your iPhone ?
If at this point the Mac version still can't even call your iPhone try this:-
Quit Messages if open.
In the Finder > GO Menu > Go to Folder enter ~/Library/Preferences in the dialogue box that appears.
In the Preferences find the com.apple.ids.service.com.apple.iMessage.plist and the com.apple.imessage.bag.plist
Drag both to the Trash.
Restart Messages.
The first of these .plists holds the Apple ID and the "Aliases" you use with it (according to your Mac's version)
The second holds the server iMessages was trying to connect with.
Deleting them and restarting the app will "refresh" them by creating new ones.
You will need to Add your Apple ID.
Once you can iMessages your own iPhone then add (Sign In) the Apple ID in the Messages setting on the iPhone.
You should then get the Pop ups on th Mac version which you need to Accept about the info for the iPhone.
8:37 pm Friday; July 18, 2014
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