RCA D52W20 overheating?

I have had a rca 52" projection tv for about 3 years .A week ago it wouldnt come on when I pressed the power button after unplugging it for a few minutes and plugging it back in it seemed fine.this happpened for several days now the  thing shuts off by itself and when I go to unplug it, it seems quite hot. It still comes back on after leaving it unpluged for a few minutes. Does any one have a clue what the problem could be and what the average repair cost should run?