The hard disk on my Windows XP desk top system failed several weeks ago. I installed a new hard disk; loaded a clean copy of Windows Vista, from my Dell Laptop Reinstallation Disk; and reloaded all program and backup files. Today, Microsoft says the product key is invalid for activation. Apparently, the reinstallation disk was only valid for my laptop. Microsoft no longer sells new activation product keys for Vista, since it is no longer supported. Is it safe to assume that if I buy Windows 7 Home Premium Upgrade Family Pack that it will work on my desktop computer?

Yes, it should work. In fact, I believe it is even possible to install a fresh copy of Windows 7, select the '30 day trial' option whilst installing, and then 'upgrade' from that by reinserting the disk and entering your product key the second time around.