Thank you for posting your question on Just Answer! I will be happy to help you with this problem. First make sure to hit the menu button on the TV's remote and if 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 backlight 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 backlights around 150.00 and power supplies around 100.00. Well this should help you friend.
Good luck friend, and if unit works fine, feedback and a bonus will be appreciated
Here is A link to better understand the inverter.
A good trick would be to spray each board with freeze spray and see if the unit stays on longer if so you found your problem, or a hair blow dryer to make fail quicker.