Make sure the "Max FPS" setting is set to Auto or some value. Don't turn it off. This setting might be on the main menu or it might be in the game.
If you turn it off, the game renders at a constant number of frames per sim-second. I think it's using the video refresh rate.
This has the effect of making the game run in slow motion when your framerate drops and faster when your framerate gets faster.
I think this setting acts like a "timedemo" in the Quake games.
Benchmarking is what led me to notice how the "Max FPS" setting affected the game. You want it enabled when playing the game, the only time it might make sense to turn it off is for benchmarking.
I've benchmarked Driver on a K6-3+ 450MHz with a Geforce2 MX. In a repeatable scene, I was getting 17-18fps on the Ultra preset with max traffic density. This was with NVidia drivers 5.32 and 8.05. I also have tests logged with v45.32 where it was a bit slower at 16fps.
It was basically the same framerate for any resolution so it was apparently CPU limited.
Side note about benchmarking - I noticed that the behavior of the cars in this game is deterministic. If you follow the same steps each time you run the game, you'll get the same stackup of traffic every time. In my spreadsheet I recorded what traffic pattern should be seen so my tests are comparable.
Your Tualatin + Geforce2 Ti should have no problem giving a good experience, but based on what you've said, maybe it's dropping below 60fps.