Can you give me the model number? I will check my repair data base for know problems.
When it shuts off does the power light blink, how many blinks before a pause .
The model is 6615LF4 made in 10/2005. When I put the TV in video 1 mode to play DVDs and start the DVD player the LCD screen on the TV looks great but then in a few seconds the TV screen goes dark. If I push the power button the screen goes back to normal for a few seconds and then goes dark. I have not seen the power button blinking. It is like the TV is not getting power to stay on. The same happens when I put it in video mode 2 to watch TV. I get TV for a few seconds and then the TV screen goes dark. The DVD player and analog converter are all pluged into the same electrical strip and they are getting power and working.
I believe from your symptoms that you have a bad back light inverter board, or bad capacitors on you power supply.
In this set one board is used for both the inverter and power supply.
You can order from Parts Store for $48.95 plus shipping.
If you are fairly technical , you should be able to change the board.