Is it a Panasonic? I had the same problem with mine while it was on warranty. Panasonic sent a tech to my house, he opened the back changed out most of the screws holding the PCBs to the housing. It mostly solved the problem, there is still some audible hum but it is really faint.
The issue was a loose transformer on one of the PCBs. They change all the screws just to be sure that it won't occur again on another board.
You can tell if this is your problem, if the hum becomes louder when the screen is white. My hum was coming from the top left corner.
Good luck, it is really frustrating!