FaceTime "signing in" forever (version 2.0, OS X 10.8.5)

When I enter my Apple ID and password into FaceTime for OS X and click "Sign In", the status indicator says "Signing in..." and the circle twirls around... and nothing ever happens after that. I literally let it spin for about 10 minutes on my last attempt.

I have totally used FaceTime before, so I know it used to work at some point.

FaceTime gives no feedback to help me narrow down the issue. I have no clue.

Yes, I do have internet connectivity (which I'm using right now to post to this forum).

version info: FaceTime 2.0, OS X 10.8.5. (No, I'm not on Mavericks yet. I will soon, but I can't right now.)

Anybody know a solution?