It would be nice if you could post info on your specs, like your graphics card and version of Windows. To me it sounds like a driver issue, are you sure you have the latest drivers for the graphics card or a known good set?
Also, if Project64 is capable of it you might get it to work fullscreen if you start it fullscreen, and not switch from windowed mode.
Finally, if it gives out a normal Windows General Protection Fault, it would be nice to know what module it crashes in if any (eg. PROJECT64.EXE has crashed in SOMEGFXCARDDRIVER.DLL)