I have used a product - XPSyapad - on numerous occasions to obtain the Windows &/or Office product codes prior to reinstallation of same or for authentication purposes. Here is the download site:
http://www.xtort.net/xtort-software/xpsyspad/
After download and install, select "Admin" from the top left. Then from the dropdown menu select "Retrieve Windows Product Keys". That should be it.
Let me know how you make out.
Regards...