Yes, i believe you can, however i think crysis 2 has a DRM secutiry system so if for some reason you can't install it, maybe its because of the DRM, in that case you should call EA for help
I havent tried installing the game yet and putting the key in, but maybe I should just do that first?
I would suggest that what you do FIRST is to de-authorize the game on your old machine. Check http://activate.ea.com/deauthorize/ for info how. Do this before you install on the new machine, and you should be able to authorize the new one no problem.