I'll share my story: Might help... might not.
My TV also shared the same fate. While moving houses, my girlfriend and bro thought it'd be a good plan to pack her snowboard in next to my LCD for the drive. Well the edges did a number on the plastic and I cried myself to sleep that night.
I ended up going out and getting the finest grit of sandpaper I could find (2000+ AutoFinish stuff) with the intention of buffing out the scratch. So with a little water and a lot of wax-on/off, I was able get the scratches down to nothing by continually re-applying water to the area! This did however take a good bit of the Anti-Glare layer off of the plastic.
So not being completely satisfied with the job: I then applied a little Brasso, to smooth out the remaining marks left by the sandpaper, let that stand for a minute or two and then polished the screen.
The result was not ideal but the scratches were gone: While the TV was on (and it wasn't sunny outside) you couldn't tell that there was anything wrong with the screen. While the TV was off and/or it was bright outside, you could see the difference in sheen.
Long story short I ended up returning the TV back to Costco the day before it's anniversary and exchanged it for a Samsung LNT4032H... they didn't even ask about the interesting mark on the LCD