Windows XP Serial AND Product Key Change?

I have a dell dimension with a good COA on it. The COA, as you know, has two numbers/keys on it. the Product Key, and what I take to be a serial number.
This is for Windows XP Home Edition.
The OS was reinstalled on a clean drive using not Dell's media but a Retail disc that I have from another install.
So, I need to change both numbers/keys to what is on the COA.

All the info I have been able to locate thus far [tons of it] ONLY deals with the Product Key. I have to get these both to matchup as legit. How do I dig out that other key/serial number and change it while i'm changing the Product Key?

thx
z

 

As best I can tell, that other number on the COA is called the "Product ID". Trying to search this topic is maddening, because all these terms: ID, serial, product type, etc seem to get dumbed down to just "Product KEY" so I get the same article or text copies thereof on every google attempt!

if anyone can correct my terminology, please do. The "ID", as i'm calling it is [on this dell system] the string of digits/characters just below the barcode

 

thx for the note, Halo, but it turns out I got 'er done w/o reinstall.
Got it done.

For future folk with this sort of issue:
- sicko machine that needed a nuke & reinstall. Dell Dimension with COA but no media
- nuked the drive. used a Retail XP Home Edition SP3 CD that was the only "Home" version I had in my disc stash
- During install tried to enter the legitimate OEM key and it failed. Blanked it and went ahead with the install. Everything came up ok. Loaded the Dell drivers etc [had stashed in an aux hard drive]
- Much to my surprise, downloaded the MS "Change Product Key" utility, installed it, changed the key [and actually made a mistake - entered the key for yet a third system unknowingly], it accepted, ran its scripts, restarted the system.
- Then went to Activate where I discovered the OEM key used with the Change util was not the same as the COA sticker on the box. Entered the RIGHT one in the Activation step, system activated and life is Good. and Legitimate.

I guess if someone had written this up and posted it somewhere, I would have had huge doubts that it would work, but it did. It would be educational to know how MS's little tool works - it must pickup something from hardware and spin a new and somewhat loose ID....