Hi Lee, Do you have an LG service remote - an invaluable tool for recent LG TVs? Press the IN START button then if the menu appears, select POWER OFF STATUS. It will give a log of the power-offs and the cause.
Check the psu-main connector on the PSU and see if you're getting a 3V+ INV. ON signal at switch on and see if it stays there. If no signal, then the main board is faulty. In which case cooking will usually restore it, but this is seldom a permanent solution.
I'd also suspect the backlight LEDs. Common in LGs. Bruce