Hello Dan, and welcome to Seven Forums.
If you have a OEM Windows 7 version, then you will not be able to install it on the new computer since it was permanently tied to the old computer when activate on it. If you have a retail Windows 7 version, then you can do the optiom below.
If your using the same hard drive in the new computer, then you can just do a clean install
to format it and install Windows 7 on it. Since that Windows 7 key number was activated on another computer you may have a problem with doing a normal online activation. If you do, then you can just do a phone activation
Hope this helps,