If I am reading your post correctly, the TV starts out with a problem and then corrects itself after a while?
If this is true, I would suspect either an IC that is sensitive to heat or there are connection problems somewhere in the video path. As oldTurkey suggested, try re-seating all of the cables first. Any dirt or corrosion within a connector can cause this type of failure.
You can narrow this down a bit too with a simple test: Does the menu appear correctly at all times or does it too fail in the same area? If the menu works but the standard signal does not, then the problem is in the logic board and is not a display problem.
Update this when you can.