Bad news, you will need the key to install Windows.
When you reinstall Windows, it deletes all information about any previous installs and asks for all information again, including languages, time zones, and authentification codes.
Unless you can find the install code, you are stuck.
You may want to look on the PC case side or bottom to see if there is a Windows sticker, or on the case that contains the CDs.
The only other option is to get a new version of Windows and a new code.
Hope this helps,