Messages/FaceTime broken in 10.8.5
Ugh. Both Messages and FaceTime are broken for me in 10.8.5; they've always worked flawlessly before I updated. I've seen all the similar issues people are having, and none of the fixes I've found are doing it for me.
Symptoms in Messages: I sign in with my Apple ID on the "Accounts" tab in Message preferences. I get a pop-up window asking for my iMessage Password. I enter it, and immediately get the same pop up window again. As long as I keep entering it correctly, it keeps asking me for it again. If I enter my password incorrectly, it gives me an "Incorrect Apple ID or password" error as you'd expect.
Back when it worked correctly, I never got this pop-up window. All the login activity took place inside the "Accounts" tab.
I created a second user account, and I can't log in there, either. But I don't get the pop-up. It just gives me a message about not being able to connect to servers, please try later (that's what happens when I try to log in to FaceTime, too).
I've tried deleting all relevant plist files in preferences, changing my Apple ID password, and everything else I can find suggested in the forums. Nothing seems to be working.
Again, everything was working fine in 10.8.4 and earlier.
Any ideas?
Mac Pro, OS X Mountain Lion (10.8.5)