Have you tried running Generals under XP SP2 compatability mode? If you find the shortcut or .exe file, right click and go to properties in Vista there is a "Compatability" tab which allows you the run the program in a compatability mode down as far as Window 95. That might get it to work if it worked on XP before. Also the Generals manual suggests that some anti virus software or crash-guard software can cause problems when running it.
I tried running it on my Vista laptop but got blue screen/stop errors which I think is a hardware problem as compatability mode didn't help.