Television and Home Theater

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?

Three nights ago, our power flickered off and then right back on during the night which made the TV go off.  I tried turning the TV back on and the little green power light keeps flashing and will not go off.  I have unplugged it several times, waited for 25 minutes to as long as 8 hours, but once I plug it back in, the little green power light will not stop blinking.  My power button will not turn the tv on until the green light stops blinking.  What could be the cause of this?  How much does this type of repair cost?

we have an rca f32665 tv the catv connector is loose but i get a picture-the problem is that when i connect the out cable from the converter box to my VHS deck and then to the tv i get this message"NO SIGNAL AVAILABLE". THE CABLE COMPANY told us that we have a bad RF connector?? is this something that can fix my self?? where can i find tech info as far as parts numbers, schematics etc... i been using the video-audio connectors from the cable box to the connect to the TV's audio-video connectors to get a picture and sound.