The situation also happens in big corporations which have volume licensing (VL) agreemnts with Microsoft, which tends to use a same VLK (Volume License Key) or leaked product key to activate all computers.
To enter and make use of the new product key does not really require whole fresh re-installation of Windows XP.
I have a license from the previous computer for Pro.
When I went to do a clean install of Pro the computer ended up with an activated version of Home (because that is what the key in the BIOS is).
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Here we explain how you can programmatically determine whether the version of WUA that is running on the computer meets your needs, that is, whether the version is the latest or at least current enough.