There is a couple of different things that I can think of that could cause this problem...HOWEVER the problem is that the minimum that I can think it will cost is around $225 so I don't think there is going to be any feasible way that you are going to get this set repaired. I truly am sorry to bring you the bad news, I do think it is in your best interest to get a new set.
I think you could have a bad power supply (about $225 repair), bad main board, about $400 repair, or a bad LCD panel, about $1500 repair, (yes, I do mean $1500, the part alone is $1100!!)
Again I am sorry to bring you the bad news, please let me know if I can do anything else for you.
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