Is this illegal? (PC's)?

I recently pulled my really old 2004 PC out of the closet. While I was inspecting it I noticed that it still had the Windows XP Home Edition product key and certificate of authenticity on it. I want to install Windows XP on one of my newer PC's because I know that XP is way faster than Vista (and I think that those product keys can work at least 2 or 3 times). The problem is that I lost the Windows Vista Home Edition installation disc a long time ago. Is it legal for me to download an ISO of the installation disc (probably from the Pirate Bay) and then use my purchased product key to activate and install it?