Sorry, not run into that one. I have been using Win7 for a long time, with no problems on C3C. I have run many of the custom maps and scenarios. I would check my desktop settings and make sure it is one that C3C can handle.
If it is notone, try using the Keepres and video:
KeepRes=1
Can be 0 or 1. If 1, your screen resolution is used for the game instead of the default 1024x768.
Video Mode=1280
Can be 1024, 1152, 1280, 1600, 1792. Changes the game's resolution to the value specified (instead of the default 1024x768).