I have a copy of Test Drive III: The Passion, but whenever I run it in my Windows XP machine it runs too fast. Is there any way to run this game in a modern computer?
There is a DOS emulator called DOSBox that supports this game. Get full details on DOSBox support of Test Drive 3 here, along with some helpful comments.
You can download all the Test Drive games for free at abandonia.com.
There is a program called Mo'Slo that will slow down games for you so that the become playable on modern hardware.
You already have [dosbox] tagged. Have you already tried Ctrl+F11? This tutorial has some more tips.
You also have [abandonware] tagged. You should probably know that the legal standing for that is about as firm as piracy of modern games. Which is to say, it's the same. Just old.