My LG 42"tv shuts off by it self

Hello, The best way to fix this is by opening the back cover of the television set.
The power light may be flashing or if you are runing with a series light bulb it may be cycling on and off continuously. There may be a chirping or clicking sound from inside the set. (Note: using too small a series light bulb load during testing for the size of the TV may also result in this condition.)
If there is a low voltage regulator or separate switching supply, it could be cycling on and off if the horizontal output, flyback, or one of its secondary loads were defective.
Does this TV have a separate low voltage regulator and/or switching power supply or is it all part of the flyback circuit? For the following, I assume it is all in one (most common).
Some simple things to try first:
Verify that the main filter capacitor is doing its job. Excessive ripple on the rectified line voltage bus can cause various forms of shutdown behavior. An easy test is to jumper across the capacitor with one of at least equal voltage rating and similar capacitance (make connections with power off!).
Use a Variac, if possible, to bring up the input voltage slowly and see if the TV works at any point without shutting down. If it does, this could be an indication of X-ray protection circuit kicking in, though this will usually latch and keep the set shut off if excessive HV were detected.