Just an aside....it is an LG?? Is the light on the top okay or is the plastic casing around the light melted??? If so, the door probably wasn't left open.
There is a known problem with the LG french door refrigerator where the light switch malfunctions and the light doesn't turn off even though the doors are closed, and the casing around the light can melt (and the temp. inside the fridge goes up and ruins all the food inside). It happened to me about a year ago with my fridge.
It looks like this:
http://www.thriftyfun.com/tf62504889.tip.html
If this is actually the problem, call LG. They will send someone out to fix it.
Just at thought....