Power comes on but turns off, when back is removed

So the 12V power supply is either not there (faulty power board) or is shorted by whichever board it is passed to.

I do not know this particual Sanyo, but I know what I'd do - I'd open and see at the power board which of the output cables carries 12V; they are most commonly labelled on the power board, right next to the output pins.

12V is usually power going to the audio amplifier and sometimes to tcon (LCD controller) of even the main board , but it won't go to to the ysustain - the other apparently large board when you open the TV.

Of all listed I'd say only the audio amplifier is likely to short...all others are possible, but highly unlikely.

BTW what do you mean "but turns off, when back is removed"?