Unfortunately, there are three components that can cause the problems you're having.
I will try to explain this the best that I can here.
There are several things which could cause your problem. One is the Mainboard, the other is the T-Con (LCD Timing controller), or the Backlight Inverters.
As a quick test to see which board is causing the problem, disconnect the Backlight Inverters from the supply and see if the TV will power up without them connected. If so, you've found the source of your short, and would replace the backlight Inverter.
If the symptoms are the same with the Inverters disconnected, then you'd want to disconnect the two ribbon cables connecting the mainboard to the T-Con board- which is the small 5" x 7" board mounted at the center of the LCD panel. If the set powers up and stays on with the T Con disconnected, then you'd replace the T-Con.
If the set acts exactly the same whether or not the T Con or Inverters are disconnected or connected, then your mainboard is suspect, and the only board that you can't really test. The Mainboard works in tandem with the power supply to produce the rated voltages responsible for the TV turning on/off.
The link below is where you can visually identify, as well as purchase replacement boards for your TV:
If you need further assistance, simply reply back and I will be online later to assist you further (I have to step out and pick up my daughter right now).
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