I worked out specifically what was going wrong with my Q3A. It's the NVidia driver settings.
Quake always works when they're set to High Quality and it always fecks up when they're set to High Performance.
So, setting your card to High Quality should fix it for you. You can use the latest drivers.

I had the exact same problem today. I rebuilt my machine and Quake's graphics went mental. Wavey coloured lines, undecipherable text, all that. I solved the problem by installing nForce 94.24 from nVidia's site. I hope that works for you. **UPDATE** After I made sure Quake was working with v94.24 fo...