Turn the TV off for awhile so it cools down. Now turn it on, then squeeze the bezel of the TV (the outer trim piece) applying pressure to the TV's display panel, near the affected area.
Does that clear up the screen, even if it's just for the few seconds you have pressure applied?
Without a decent working knowledge of electronics and test equipment (a voltmeter, at the very least), the only thing you can do at this point is unplug the TV for a few hours. Sometimes these issues are just "glitches" that can be cleared that way.
If this doesn't remedy the issue, you definitely have an internal failure here. Without making any measurements inside the TV, it's tough to say what the issue is but there are only a few parts inside these models that could cause this: The power supply, the main board, or the LCD panel itself.
So if the unplug doesn’t cure this, consider having a tech take a look at this. Some diagnostics wouldn't run more than $100, and most of that would be put toward the final bill should you decide to have it repaired. A typical repair for something like this would be $250-$450.
If you'd like, feel free to post back with your zip code and I'll see if I can find a tech near you.