I have Vista and my GC works fine. A lot of vista users have this problem on the official forums, so check there if I fail at explaining.
If nothing comes up after you hit START in the blue or whatever colour box it is, then right click the Grand chase Icon.
Go down to preferences and (I kinda forget what to do here now, because I'm on my brother's sucky laptop that doesn't have GC) go through the tabs and try to find a drop down box at the top of one of the tabs. I think it says run using preferences for or something like that. Anyway, if you find that, change it to Windows XP.
Now just rightclick again and hit run as administrator.
Avarice, AKA ByakuyaZ.