If there is problem with an inverter or a back light, the lights will come on for about 2 seconds and then shut off.
The Sanyo DP42484 television has a problem with poor quality back lights. I had one that had three bad back lights. I replaced them and it fixed the problem. The TV now comes on and stays on.
Replacing the back lights is a very tricky problem. You have to completely disassemble the entire TV to expose the back lights. The hardest part is removing the LCD glass without damaging the very delicate ribbon cables that connect it to the rest of the TV or cracking the glass.
You then have to reassemble the television, except without the LCD glass. You can then power up the TV and see which back light are not illuminating.
The back lights are 950 mm long and 3.3 mm wide. There are 12 of them. The ends are coated in a silver paint for conductivity. They are held by metal U-shaped sockets at either end. In the middle of the length of the fluorescent tube is a C-shaped plastic support to hold up the center of the long tubes. This plastic is very brittle and breaks easily. Try to slide the tube to the side thru the plastic support. If you try to spread the support wider and pull the tube foreward, the C-shaped plastic support will break.
I searched for an exact replacement, but I was not successful. The closed I could get was 950 mm long and 3.0 mm wide with wire ends. I purchased these from http://www.ccflwarehouse.com for $25 each. Part number CC30950. I bent the wire ends back and soldered them to the metal sockets. When the 3 bad lights were replaced the Television came on and stayed on.