Unfortunately, all TV models have a failure rate, usually in the low single digit percentiles. If your TV worked for 3 years and then started to break, that is outside almost all manufacturer/store warranties if you didn't also purchase an extended warranty. Some TV manufacturers have higher failure rates than others, so at least you can minimize your risk of your expensive new HDTV being a lemon.

I know it is in the past, but LG plasmas (especially 3-5 years ago) have huge reliability/failure issues, which are documented online in forums (like you said). I'm guessing you will be stuck with buying a new TV since LG and Sears will not help you out. When you buy a new one, go for a company with better reliability rates and also check out Costco since they double the manufacturer's warranty for no extra fee.

I'd shoot for Sony, Samsung for LCD (maybe Vizio if you get it at Costco), or Panasonic for plasma.