"There is a flex ribbon cable from the display to the main board inside, you need to remove power and pull the cover off, remove and reseat that cable a few times, should clear it right up, for a while"
Another tip from the same thread:
"Oh and FYI if it keeps dying like that use a pencil eraser and gently rub the contacts on the cable to clean them and work it in and out of the jack a few times and then clean the cable again to remove anything it pulled off the jack pins. You can also use stuff like contact cleaner or de-oxit that leaves a protective film but i don't think its corrosion so much as it is coming loose over time. I have seen a lot of the 780, 785, 796 models with this problem after being used mobile, but even one at home on a desk that gets bumped a few times a day seems to suffer from it. In one extreme case i used a bit of hot melt glue to keep it in tight after cleaning."