This is not a Parallels issue. This is a Microsoft licensing issue.
In the "good old days" any Windows license sticker was acceptable. These days, MS has changed their terms with OEM providers (which most OEMs were not happy about), and they also changed the End Use agreement.
In short, a copy of Windows that comes with a Dell is only licensed to be used on a Dell computer. Migrating that license violates Dells agreement with MS and the EULA you implicitly agreed to when you used the machine.
Having said that, my experience with refurbishing machines for charity (old machine discarded by companies) is that if you call in to MS, and he license number is not already in use by 100's of other machines (ie.: not pirated) then they are happy to re-activate it. I have been telling them that the reason for the re-activation was a replacement of hardware - without getting into details. Sometimes too much information is a bad thing.
Of course, this means that most of these machines are not legally licensed. Even the ones that were Dells, because I typically install from a generic OEM CD I created that has SP3 and other goodies preconfigured, and the license agreement likely specifies Dell's OEM version. I'm not too worried because historically, the anti spyware "righteous cause" seems to only go after people or companies with lots and lots of money they can settle for out of court.....
You might be happy to know that there are companies out there salvaging license stickers from old machines. Heck, from the thousands of machines destined to have SP but were hastily refurbed with Vista - they did not bother to remove the XP license stickers. So there are lots floating around. In Toronto, the going rate is around $80 for a pristine Retail copy, and around $50 for a good OEM likely used one. I bought stickers for all the MACS I have running Parallels. Although these prices will go up as supply drops.....