It is quite safe to reinstall Office 2003. The activation issue only comes into play if Office has been installed on more PCs than the licence allows. Reinstalling on the same PC multiple times does not impact the activation entitlement.

Since you have the original media, all it takes to make a backup is to insert it into a CD/DVD drive and copy the files to another disc (of any kind).

As for SP3, there were many patches released after that. If you install SP3 on a new system, Windows update should soon alert you to all the updates it needs to bring SP3 up-to-date. You could then download those updates.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]