42" LG Television - faulty

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42" black LG TV Condition: For the first half an hour after turning the TV on, the picture quality is poor and only just watchable. After half an hour or so the picture improves, but the top quarter of the screen is still fairly dark. We have been leaving the TV on all the time to remove the need for the half hour warm up and it doesn't seem to use much electricity. We did this for about a year or so - it's fairly workable - but have now won a new one in a raffle so want rid of this one. We have been told that we might be able to buy a part online which would resolve the problem, but I haven't looked into this and don't know whether it is true or not.