HELP with on & off black screens

Screen turns black & on in a random order.  Some flashes on and off at a rate of secs, sometimes rate is slower, sometimes seems completely random.  Sometimes stays black for hours; sometimes stays on for hours.  Black screen changes to pretty picture that says NO SIGNAL. Have turned router & set top on and off in every conceivable order more times than I can count.  Have checked all connections. Spent hours last week trying to get help - couldn't even get problem recognized.

HELP!!!! Please send someone out!