Unable To Sign Into Messages

I would love to run Messages on my Mac, but for some reason it refuses to recognize me. I seem to be signed in ok on iCloud. And my iCloud and Messages works fine on my iPhone. Here is the string of error messages that pop up when I try to launch the Messages app.

So I got to preferences and sign in with the password, then I get this...

The password has been updated, but nothing seems to satisfy Messages. I always end up with the same pop up:

Nothing I do seems to make Messages work anymore. Any help is appreciated!