It probably won't work---at least the one that I got foisted on does not because the hardware in a dell and what on your new computer will be radically different---but it also will depend on version--be it upgrade, OEM, or full.---but its my understanding that the OEM license marries the install disk to the motherboard.
But as Blade Venom points out---if microsoft lets you activate it--you are in pretty good shape. And will never rise to the occasion that at 2 am they will come for you and maybe break an arm or two. Unlike the mafia goonish tactics of the RIAA.