By "old" I mean around the mid to late 2000s.

What I remember is that you could buy parts for your car that would help it to perform better in races. From upgrading parts like engines to maybe purchasing something like ice resistant tires if you were going to compete in a race that had ice?

It may have been online with other players but it's possible I just thought that and that the other cars were just NPCs.

I don't think you actually controlled the car yourself, at least not in a traditional racing game sense. It's possible that you just enter it in the race and it does it's own thing, or maybe you could select options to perform during the race. I'm not sure.

You saw the cars and the race either from the side or top down.

It may have been a Lego game with Lego cars.

It was free to play. Just on a browser. No CD or anything needed.

Other games I would have been playing around the time and that my memories associate this game with would be a bunch of games from the Lego website, like the Backlot game (3D graphics game running around a studio backlot doing little missions), a Bionicles point and click RPG style game, a game where you can control a Lego(?) RC car around what looked like an empty store with a bunch of ramps, and a browser game based on a Gorillaz music video where you drive a car around a raised road that does loops and stuff.