Didn't we learn in the first movie that Tony Stark's armored suits are powered by the miniature arc reactor that he wears in his chest to power the gizmo that keeps his heart beating? This would include the second suit he built, the Mark II armor, in particular.
So how was James Rhodes able to operate the Mark II suit in Iron Man 2? If Tony wasn't wearing it, it wouldn't have a power supply.
My geek-fu is still strong.