If it's an upgrade key, then you need to install the old OS and then go through the upgrade installation rather than the full installation. I have issues simmilar to this, so I've gotten used to keeping install files backed up on a different drive and when I install my windows I disconnect my other drives.
So, putting 8.1 on a new disk is the same upgrading it? Man, that's annoying. So I guess the question becomes, "Can I install Windows 8 then upgrade to 8.1 without buying a whole new copy?"