I had a 2001FP about 2 months ago. It arrived with a brown line on the screen starting above the power button and gradually fading as it went toward the top stopping about 3/4 of the way up. I called Dell and they had no problem sending me another one but they were out of them at the moment so I had to wait a few weeks. During that time I realized that I didn't like the LCD so I called and just returned it instead.
My reasons for not liking the LCD...
1) LCD lag. Yes, the 2001FP is the fastest 20" LCD out there but it still suffers from lag with fast moving video or gaming. There was a point in Half-Life2 where I was watching water flow by and it was all pixelated. I think that was the straw that broke the camels back for me and my 2001FP.
2) Price. My current monitor (a 22" Compaq P1220) was $250 on a deal. The 2001FP looks great, especially with text @ 1600x1200, but it's not $350 better and my CRT blows it away in colors.
3) Screen door effect. Not a major gripe but it did bother me because my desk is not very deep so I sit closer than most people.
Benefits of the 2001FP over my 70lb CRT...
1) Space, weight, and adjustability. The 2001FP is thin, light, and can be easily and quickly positioned.
2) Power. The 2001FP uses much less power and ran much cooler than my CRT.
3) Brightness & sharpness. There's just nothing better than razor sharp text at 1600x1200 when you're viewing web pages or working with office apps. I miss that but I'm usually using my lappy when I'm working.
4) No horizonal damper lines. Honestly I barely even notice them on my Diamondtron tube and even then only if I'm on a bright white background. But they are there and some people are bothered.
To the original poster, if you can't fix the stuck pixels I say return your LCD now while you're still under the initial satisfaction warranty. For $600 I would want a perfect screen and it would be worth it to me to pay the return shipping for a screen without dead/stuck pixels.
Good luck