FaceTime will not “verify” my email address

I have used FaceTime on my Mac many times, but now when I try to log in to use it, I keep getting the message, “FaceTime Activation - Could not verify the email address.” I tried using an alternate email address and still got the same message. I logged in using my Apple ID and even changed my password and Apple emailed me back promptly (showing that Apple acknowledges my email address as valid) but I keep getting the same message!