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The likely problem is bad capacitors on the power/inverter board, to check for them you will need to remove the back cover, there will be a few screws holding together so make sure you find them all, some can be hidden under stickers or rubber incerts, before opening the set unplug from mains, and leave for about an hour or two in ensure the caps inside have had time to drain the voltage, once you have taken the back off the set you will see pcb boards and a few wires, your looking for cylindrical barrel shaped componants on the the board with silver tops, if any of these show signs of leakage or are slightly domed or pretruding at the top they are faulty and will need to be changed.
You will need some soldering skills to remove the capacitors from the board, and replace with the new ones, you can buy the capacitors from places like maplins or other online electrical componant shops such as RS Componants, ensure you know the value of each faulty capacitor, it is written on the side of them it should be somthing like this 25v 47uf, V stands for the voltage, you dont have to exact with voltage as long as it is equal to or more than the voltage stated on the cap, the uf however stands for micro farad and needs to be exact, if the cap is 47uf then you will need to replace it with a 47uf value cap, if not it will not work and may blow, the same if you get a lower rated voltage cap. Also before removing the old caps from the board make a note of which way around they are placed on the pcb board, they will be markings on the side of the cap to show which leg is the negative side or cathode, it will also be marked on the pcb itself. If you get these the wrong way around then the cap will blow. Hope this helps and post back if you need any further help.