If you have Regestered/Activated the first key with MS (and it is a legal key) then you can call them up and advise them that you have replaced your PC or formatted it etc and reinstalled your OS.
In which case your old key will be re-issued for activation and you can then just install SP3.
This situation will resolve you issue, unless of couse the first key is still in use on another PC!
If so (and this is an additional PC with an additional instance of XP) then you will want to read on.
So...
You can change you windows product key after installation as described in this KB on the MS site:
http://support.microsoft.com/default.aspx?scid=kb;en-us;328874
However, if i were you i would just reburn my media (your SP3 disc) as long as it is LEGAL and within all copyrights etc!
If it is a downloaded and LEGAL ISO then redownload from you supplier or Technet or whereever you purchased it ...
but this time burn it sloooooooooowwwwwwwwwer!
As your error sounds very similar to a disc being burned to fast! ISO's need to be burned on a very low speed setting, usually the slowest speed available is advised.
If it is an illegal copy, dont tell us anymore!
Phreak