It is the product key you want. If you have not yet uninstalled it you can get the key from the registry using Belarc Advisor -
http://www.belarc.com/free_download.html
However it is rare that re-installation achieves anything useful that simply repairing Office will not achieve.
Most corruptions relate to the various user files, and that corruption will remain over re-installation.
You haven't said what form the corruption takes, but for Word, see -
http://www.gmayor.com/what_to_do_when_word_crashes.htm then
http://word.mvps.org/FAQs/AppErrors/...artingWord.htm