The TV turns off and then on automatically

unplug the tv and let stay unplugged for at least 24 hrs then try it if that dont work then it sounds like a power board issue

Please check your capacitors for malfunction. Replace them if needed.
Regards

Do you have the tv connected by any scart connections.
If so turn them of 1 by 1 as the scart can control the tv in stand by.
Also when you turn of remove the batteries from the remote if this cures your problem replkace the remote

Power supply problem. Any light coming on at all? in the front panel or visible from the back through the case?

Bad x-address board.

Contact LG for service. 1-800 243-0000
A capicitor on the main board has cracked causing the issue.
A simple fix.

I try to turn on the TV but green light turns on then immediately back off. The TV is 3 years old 50" LG Plasma

Take the back off with no power connected..You should have 2 invertor pcbs..one on the left and one on the right..well the side of the picture you cant see is the same side of the faulty invertor..replace this and this should solve the problem.it is the cheapest option..if not..im afraid is is a new LCD screen unless you are prepared to take it appart and replace backlight bulbs :)

bad panel

If the Video (Picture/Pix) is gone but you can hear the Audio (sound), then it could mean the YSUS PCB Assembly is gone/kaput/finish. Can replace the PCB, not repair the PCB due to timing circuitry involve. Cost maybe roughly $500 depending where you located. The PCB is located on the left hand side of your TV when you are facing the back (Back open). Might find 3-4 brown flex membrane connecting to the plasma panel. The PCB has a silver or black aluminum heatsink (big) on it.
Good Luck.