Hello friend, Thank you for posting your question on Just Answer! I will be happy to help you with this problem, And possibly help you save on these Labor charges today, So please don't Accept my answer unless you are satisfied,
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First make sure to hit the menu button on the TV's remote while the screen is black, and if you have sound, and nothing is there then friend while the set is on turn a bright flashlight on and shine at angle into the set push the TV menu button if you can see a image then your back light is not working. You can also check the transformers they are close to were the wires plug into the panel, make sure all transformers read the same amount of resistance if not you have found a bad one. Now you will have to check to see if the power supply is sending 24v to the backlight, if not the power supply is bad. Cost back lights around 150.00 and power supplies around 100.00. Well this should help you friend.
Here is a link to better understand the inverter. Within the power supply the capacitors
Well Good luck friend, and if my efforts on trying to help you save on those large labor charges are appreciated, feedback and a bonus will be appreciated