It's probably one of two things. Actually it's most likely both. I had the exact same problem and here's what I found.
1. Must be S-video from the card to the TV. Don't convert it, you'll loose signal strength. This is most likely the reason for the loss of color.
2. Geforce cards use different TV-Out chipsets from one manufacturer to the next, so there is no telling the quality of the TV-Out chip.
Here are my suggestions. First off no matter what you decide to do with the Geforce 2 card, you will never be happy with the performance until you have a TV with SVideo. It's what I've read and what I've experienced, so I'm fairly confident that a TV with SVideo will make a big difference. I'm using a Panasonic 27" CT-27D11. Works great. Still looks a little fuzzy in windows, but looks great in the games.
Second, go for an ATI card. I'm not a big fan of the ATI cards, but I'm using one in my setup and I'm quite pleased with it so far.
Hope this helps.