The voltage for a backlight on an LCD TV is "200 - 500 volts" (web search)
Not like the old picture tubes that run at 25,000 volts.
Why static would build up is beyond me. What does happen is that temperature rises. I can feel the warmth when I go near my LCD TV. After a half-hour the temperature is up. One circuit component moves a bit relative another, and a connection is lost...
When you touch it, maybe you cause a little vibration or move the TV slightly, and it connects again.
The thing is it's an intermittent, often hard to diagnose. It would be nice if it was a bad cable connection. Try to tighten or reseat any connections behind the TV, and to the set top box. When a digital TV looses signal it often goes to black screen. It's possible signal strength is low from the cable or satellite dish. If cable, and they will make a free service call, have them look at the situation before repairing the TV. There could be an old splitter in the line somewhere that makes signal strength marginal.
If it stop working, and will need service anyway, unplug it and drop it two inches to the cabinet it's on. Power up and see if it will be more stable.
