free windows 7 upgrade comes to late... help!

Hello,
i bought my pc not long ago. so i applyed for a free copy of windows 7 to upgrade my comp. however i heard nothing from them for agessssssss. so a week after windows 7 release i just went out n bought myself a copy.. now a goooood few weeks later the free upgrade arives, my question is.... can i use the Product key i got from the free upgrade to upgrade my other pc... i know the pc cd pack itself wont work on my other pc as its not a "acer"
i was just wondering if i use the windows 7 i bought and the product key from the upgrade pack if that would work.? or if theres away to rereg my win 7 pc with the other cdkey ? any help would be great ty (the_don109@hotmail.com)

T=You have to use the disks that came from the manufacturer on that computer.

It contains all the pre-installed software that came with your PC when you purchased it.

As for the other disk, you paid for it, you can put it on any computer you like.