OEM Office 2010 without media - how to reinstall?
I have tried it and it works.
Just download the trial version corresponding to the version you have, and when it asks you to enter the product key enter your key and it will complete the full install process.
For OEM keys without media, visit this Microsoft website. Microsoft will ask you for your CD key, then allow you to download the appropriate install files:
http://Office.com/downloadoffice
I work in IT and ended up calling Dell once when I was in your situation without the right installer. They pointed me to the website, and it worked.
UPDATE - Microsoft updated their link to office.microsoft.com/backup where you can get the 2010 version as well as the 2007 version (at the bottom). This site is specifically intended for reinstalls of OEM versions. There is a pretty good walkthrough of the process as well at: http://techmemos.com/setup-tutorials/reinstall-microsoft-office-20072010-that-came-with-your-pc-without-the-disc
You can use this link : https://products.office.com/en-us/buy/using-your-office-2010-product-key-card?legRedir=true&CorrelationId=a3199fae-079e-4aa3-abd1-3613f117dbfb
Official from MS