When I turn my tv on it automatically goes off.

I have three of these that I have repaired.
First you need the manual from LG. (I joined plasma-television-repair.com and downloaded it...spent the $40..it's worth it)

Don't waste your time with the Toshiba 50HP66 service manual. None of the powersupply or driver boards are in it.

The only way to figure out the problem is to start at the beginning. Pull all the connectors off of the PSU (Power Supply Unit) except for the 115 volt input. Plug in the set. If the relay clicks off the PSU is bad. Replacing it may just get to level two...Something else has caused it to fail.

If the relay stays on test the Vs and Va and 5 volt supplies. If they are good you can try reconnecting all the PSU connectors except the Y-Sustain board. It feeds the X-Sustain board. Power up the set and if the power suppy stays on you might see the controller start to run tests and blink its green leds.
Power off.

I usually remove the Y-Driver boards for the next test so as not to damage the Y-sustain if the driver boards have blown FETs.

Remove the power feed from the Y-sustain to the X-sustain and reconnect the Y-sustain to the PSU. Power-up and test the supply voltages. If the relay on the PSU kicks off the Y-Sustain might be bad. If not you can power off and reconnect the X-sustain. Repower up..voltages still good?

Using the procedures in the manual start testing Vscan and -Vy on the Y-sustain.

In two of these sets I have seen the FETs on the lower and upper Y-Drivers fail. This causes the Y-sustain's Vscan voltage to oscillate. Many people without testing just say the Y-Sustain board is bad. Don't listen to anyone that doesn't know the LG 50x3 guts of this set. If you are an electrical engineer you may want to try to replace the FETs. You can pull the driver boards off and use a multimeter to test N-channel FETs. They are in parallel so you must replace all three on both boards or they will just fail again. When one goes it puts the load on the other two and they get weak. The FET part is FQB46N15 but there is replacement FDB52N20T from digi-key that exceeds the spec. Cost for each FET is $1.34. I just ordered these and will be testing them for compatibility.

Hey if all of this is past your expertise then you can sell the set for parts. I buy them but I am in the San Francisco area and won't go too far out of my way for one of these sets.

When I turn my tv on it automatically goes off. The screen never comes on it just shuts off immediately.