I don't think Microsoft is issuing any more Product Keys for Vista now that it's been discontinued, but your PC may not be compatible with Windows 8 either if the manufacturer has no Windows 8 drivers for it, so that may not be an option.
You could always consider a Linux distro like Ubuntu. It's free, no Product Key and no activation required: http://www.ubuntu.com/ubuntu
If the machine you need to activate Vista on, came with Vista, the product will be on a sticker either at the back (if it's a desktop) or at the bottom (if it's a laptop).
If the machine you need to activate Vista on, came with Vista, the product will be on a sticker either at the back (if it's a desktop) or at the bottom (if it's a laptop).