When you remove the back of the set. You will fined a couple of caps on the power supply board that are bulged and they need to be replaced, or you can buy a new power supply at www.partstore.com. If you want to just purchase the caps, you can get them at www.mcmelectronics.com
One other thing to check to see if you have the correct voltage going to the inverter.
I have power to the TV and the on light is on and can change channels and have good sound. Wondering if it could be anything else you would as well?