Unfortunately you can't use the existing Product Key from your laptop to install Windows on a different computer. That key is "tied" to that laptop for life, as is the Windows Vista that's installed on it. Neither are transferrable to another computer.
You'll have to buy a retail copy of Windows, and that will include it's own Product Key in the packaging. Getting Vista now may prove to be a challenge, even new copies of Windows 7 are getting thin on the ground.