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There are two possible sources of this problem in this particular model. The first one and is more likely is the inverter board. This supplies voltage to the small fluorescent backlights of your TV. There are small transformers in this board which usually fail because of loose/cracked solder connections. The second one would be the power supply board. The components that mostly fail on this board are capacitors which are usually bulging or vented.
I hope this answers your question and if you have more please feel free to ask.
The parts replacement requires soldering. There might be capacitors in the power supply board that are not bulging or vented but need to be tested and in this case a tester is needed. I've uploaded the service manual of your TV and you can get it here for your reference. You can get the parts at any electronic parts supply store.