These sets are repairable.. This particular model had quite a few problems in the power supplies and Y sustain boards... However, the problem you are describing is more than likely caused by the Power supply.
These sets operate at high temperatures, and that heat will 'kill" capacitors very quickly - once they begin to fail, lots of strange things will begin to happen. This set is also known for not being able to change channels and locking out the remote control, due to the power supply failing to power other "slave" boards on the set. It is really just a case of once the capacitors begin to fail, the set may or may not send the required amounts of power out to the other boards allowing them to work together and communicate.
If you have any electrical experience, I would suggest taking a look at the sets power supply - see if any of the capacitors have a "bumped" or "domed" top - if so, they need to be replaced - you can order the new ones from www.mouser.com - just type in the values in the search box, such as 1000uf 25v 105c -
if you really wanted to take the "easy" route you could simply replace the board
The part number is: 75003044 Power PCB ASM and it can be found at www.encompassparts.com for 295.79 - just log in as a guest and search by part number.
I wish I had better news - it may be a good time to sell these sets (whether or not you choose to repair them is your choice) and replace them with new LED sets, as LED's run at a much lower temperature and "should" last longer, with fewer problems, not to mention the benifiet of consuming less electricity as well.