Apparently a lot of people can't get C1 to run on Windows Vista. Too bad.
NVidia GFX cards seem to be the problem as ATi card owners can make the game run (must be confirmed though).

Here's how to play C1 in hires mode (640*480) on Vista :
Get yourself a copy of D3DWindower-English, just google it.
Put the little progie inside C1's root folder and execute it.
First hit the + button and select Carma95.exe.
Select Carma95 in the list then press the button at the right of the computer button, these are the settings.
Make the first and second panel look like that :

Don't mind the other panels. That 640*480 value is the best as it fits C1 perfectly. However you can put values such as 800*600 or 1280*960 (those are proportional dimensions) if you want, or anything else, that won't increase the resolution but just strech the pixels.

Then yeah click OK. Press the Play button to activate the Direct3D hooking and then the Computer button to run the game~