You are allowed two activations of CS, nominally one for home and one for work, so you should be able to activate it on your new system without problems if your old PC was the only one you've installed to. The old activation will eventually time-out, I believe, so that you can re-use it on your next PC but I've no idea of the interval: unlike the system used by Macromedia for Freehand MX you don't have to (and in fact can't) de-activate your old copy.