Hey jimandlaurie224,
Check out the steps below, as those may help resolve the issue you're encountering when trying to sign into Messages or FaceTime on your MacBook Air:
"Reset NVRAM.
In case the issue is related to any of the settings stored in NVRAM, reset NVRAM on your Mac.
Check for third-party software
If you installed firewall, security, VPN, or other third-party networking software, make sure that the software isn't blocking any of the network ports used by iMessage and FaceTime. If necessary, disable the software and then try using your iMessage account or FaceTime again.
Learn more
Learn what to do if you have other FaceTime issues."
Those steps, and other steps, can be found in this article: If you can't sign in to your iMessage account or FaceTime on your Mac - Apple Support
Let us know how those steps go.
Take care!