How do you fix a broken LCD screen?

You can't actually "repair" a nick on an LCD screen. However, there are methods you can use to diminish the visibility of the nick. The effectiveness of these methods depends on the severity of the nick:

1 - Apply a small amount of Vaseline with a soft cloth or Q-tip. Wait about 10 minutes, and then remove any excess. This will fill in the nick and make it less noticeable. This is a temporary fix, and you will need to reapply the Vaseline each time you clean the screen.

2 - Rub the area of the nick VERY gently with a clean white eraser. This will also serve to fill in the nick and make it less noticeable. Do not press hard or apply excess pressure to the nick, or your may expand it and make it worse.

3 - Rub the area of the nick (again, VERY gently) with a solution of isopropyl rubbing alcohol and water. Start with a 3.5% solution (one capful of alcohol to 1/2 cup of water). You can increase the strength to up to 35%, but any stronger, and you may damage your screen. The alcohol acts to dissolve the anti-scratch coating around the nick so that it fills in. Again, this is a tricky process, so proceed at your own risk.

Personally, the Vaseline trick seems to have worked for me. Although it didn't completely cover the nick, it reduced the visibility by about 50-75% (which is better than nothing). As I usually sit about 8-10 feet away from the TV, I could really tell the difference.

While there is no way to actually repair a nick (aside from replacing the entire screen, which may cost as much as a new set), you can reduce it to where you can live with it.