Dell flat screen monitor (by 2 users)

This is a generic symptom that could happen to any LCD monitor.
The following is a generic answer applicable to most.

Two possible causes are bad capacitors or a bad light inside the LCD panel.

Open the unit and check to see if any of the capacitors in the power supply or other boards look domed or vented on the top.

Replace any capacitors accordingly. Use the same value capacitors. Most often, 1000uF 16V or 25V, 470uF at 16 or 25V, 220uF at 16V or 25V.

If this doesn’t solve the problem, try checking the surface-mount transistors on the inverter board that run the lights. Some times these transistors go bad. Check the area for any cracked or overheated ceramic or mylar capacitors.
Also, you may have a bad light inside the panel. This is tough to test without a spare light to use for troubleshooting.

You can take the panel apart and inspect the lamps but it is very tedious. It's tough enough to get them apart and back together again never mind keeping the layers clean. You have to try not to get any dust between the layers or you will see it in the picture.

There are usually two light fixtures each of which holds two lamps. One fixture is at the top and one at the bottom. Remove them one at a time and inspect the lamps to see if any are broken or very dark on the ends. If one looks out of place, it could be bad.

You'll have to find replacement lights on the net. It's not easy to replace them, but if you've gone this far, good luck. You should be able to get generic instructions off of the site that sells the lamps.