Often times it's the power supply, they use really cheap capacitors in it, and if you open the power supply, discharge the capacitors and replace them with higher grade ones, then it'll fix them.
My friend does that for extra cash on the side, he'll pick up TVs that have been thrown away and have them up and running in a day.
Ten dollars worth of replacement capacitors, he ends up making between sixty and two hundred dollars off of each TV.