Test the TV with another source aside from the FIOS box. Since you are getting that message on the screen, that means the screen itself is fine. The odd thing here is that you have sound when no video is coming though. Is the sound coming though the TV or do you have a amp setup for audio?
I've seen this come up a bunch of times at one of the pool halls I go to, after a few hours of use, the screen goes to that screensaver and they get that same hit menu key to watch FIOS message. They hit a button and the video comes back.