In order to change your Windows XP product key you first need to know whether you have a Retail, OEM, or Volume License version of Windows installed on your computer. This is called the license information and unfortunately Microsoft does not provide a way to look up the license info on your computer. So the only way to determine your Windows License is to know how you acquired your copy of Windows XP.
Here is a rough guide to quickly determine your Windows license information:
Retail: A Retail version of Windows XP comes shrink wrapped in a blue or green box that can be purchased at a store or online. A retail package comes with a CD to install Windows and a unique product key to activate it.
OEM: An OEM version of Windows is one that most likely came preinstalled on your computer, such as a computer bought from Dell or Compaq. These computers have a shiny blue/green sticker on the side that has your product key written on it. This sticker is called you Certificate of Authenticity (COA).
Volume License: A volume license version of Windows uses a volume license product key that is allowed to be used on multiple computers. This is most commonly found in businesses, government offices, and educational institutions.
Now the product key you want to change to must match your version of Windows. For example a Retail version of Windows XP will only accept a Retail product key. The same goes for OEM and Volume License.
Once again, Microsoft unfortunately does not provide a way to tell what type of product key you have just my looking at the numbers so hopefully you already know. If you got the product key from another computer use the guide above to determine what type of product key it is.