My Go Video 32" flat screen HDTV will stay on...

Question

At first my tv would cut off a few times after being on for about 5-10 secs then I get up and turn it on using the tv's on/off switch. (remote controls power button didn't work for this problem) after maybe 5 go rounds it would stay on but eventually it got to the point where it would not stay on for more than 10 secs at all. (Even after 20+ attempts) It seems like its trying to get warm in order to stay on but it won't stay on long enough to get warmed up. (I'm guessing) Its a fairly new tv that we got from a rental place and for the first 6 months it worked fine and then slowly started developing this problem. I noticed in the begging when I would turn it on and off quickly the tv would stay on, don't know if that helps diagnose the problem but anything you suggest would help. Thanks