Hello Codexrobin, and welcome to Vista Forums.
You will not be able to install a OEM Vista, or that product key number, on another computer other than the one it came with or 1st installed on.
If you have the 64-bit OEM, Vista Home Premium installation DVD, then you can use the same product key number to install it on your computer only. If not, you may be able to order it from your OEM for a minimal fee. You can use the same product key number for either the 32-bit or 64-bit version of the OEM Vista on only your computer.
Hope this helps,
Shawn