If you purchased Microsoft Office with your Dell system you would have been supplied a Microsoft Office Product Identity Card:
This will state your version of Office and Product Key. Use the correct installer from:
- Microsoft Office 2016 (First time Setup Only)
- Microsoft Office 2016 (Reinstall)
- Microsoft Office 2013 (First time Setup Only)
- Microsoft Office 2013 (Reinstall)
- Microsoft Office 2010
- Microsoft Office 2007
Lost MPI Card
Unfortunately such a card is separate from the system and Dell/Microsoft have no external record of the product key.
Follow the notes here for a lost Microsoft Office 2013 MPI Card if you reside in North America:
http://www.dell.com/support/article/ie/en/iedhs1/HOW10537 (Link is down)
All systems shipped with Microsoft Office 2007 systems and Microsoft Office 2010 systems will be outwith the warranty period and Microsoft are more than likely not going to issue you a new product key as they are looking to discontinue these versions in favour for Office 365 monthly subscriptions with 1 TB OneDrive cloud storage:
http://www.dell.com/support/article/ie/en/iedhs1/HOW10537
Thanks for the update.