Have you tried belarc advisor? It usually finds Microsoft key codes. Look at the paperwork that came with your Studio and see if the key code isn`t listed on the original paperwork. You might call Dell tech support or go online to chat support and ask them for the keycode.  

If you are using system restore, Microsoft office should stay on it. If you do a reformat of the entire laptop office would not be there after the fresh install.

That`s great news! I use Belarc advisor and print off the results. There have been times that I needed to get a driver updated and couldn`t. I could look at the print out and see the brand name of the harware and it made it so much easier to find drivers that worked.