not login on my Mac iMessage
my Apple ID will not login to my iMessage on my computer
MacBook Air 13", macOS 10.12
Messages - If you can‘t sign in to your iMessage account or FaceTime on your Mac
You can also try signing in on another device/computer. There have been a couple of posts where people's device/computer was blocked. You will need to contact Apple for that problem also.
There is a contact link.
Apple Support by e-mail or chat
Or fill out and submit this form.