I've answered three of these so far, so this problem must be a very large manufacturer's defect big among large-screen LCD TVs of a bunch of different makes.
It's a power capacitor inside the TV that controls whether the power supply works or not. Our Samsung 46-inch started doing the same thing with about 2 months of a 2-year warranty left in it, and I'm glad we called the local retailer, because they were aware of this problem and gave us the number to Samsung, who paid to send a trained repairman about 60 miles to our house to fix it. During his repair, I helped him remove the large back cover, and set the TV on its face, and asked him about the problem. He detailed to me exactly what I said above, and also that it's been a very big problem with the rush to get new TVs out to market.
If your TV is still under warranty, jump on this situation before it runs out--it is a hardware problem, not fixable otherwise...
If it's out of warranty, your local TV repairman should be able to repair this for less than $100, easy (the part on ours was a $2 capacitor, the repairman said).
Hope this helps.
LG 42LP1D 42 in....
on Feb 24, 2011