This is for Office 2013 but worth a try:

http://www.dell.com/support/article/ie/en/iedhs1/HOW10537%20

The dell would have a microsoft product identifier card or it did not come with office but rather an office trial.

Without the key you have to buy a new license.

With the key you can download the media.

https://officesetup.getmicrosoftkey.com/

The key is on a Microsoft Product Identifier Card.

If you lost this there isn't any getting it back you have to buy a new key.

As of May 1, 2013 there will no longer be an MPI card for Office 2010. If you purchase a new system after that date, you will be receiving an MPI card for Office 2013. This card is NOT backward-compatible with Office 2010 and only works for Office 2013.

The Trial Version of the software expires.  If you purchased this with the dell you have an MPI card aka PKC.

Microsoft Product Identifier card with the Key,  If you did not purchase this you must buy a key online or in a store. Office no longer ships with Disks.  If you have lost the MPI card you will have to buy office over again. You can download the Office directly from microsoft.  You cannot activate and install without this key.

Here Are The Download Locations for Office 2010 and Office 2007

Microsoft Office 2010 Download Locations

A.  Full Retail (FPP):  http://office.microsoft.com/en-us/products/microsoft-office-2010-backup-FX101853122.aspx

B.  Product Key Card (PKC):  http://office.microsoft.com/en-us/buy/using-the-product-key-card-FX101853163.aspx

 Microsoft Office 2007 Download Locations

A.  Full Retail (FPP):  http://www.microsoft.com/office/downloads/

B.  Medialess Licensing Kit (MLK):  http://trial.trymicrosoftoffice.com/msft-orpc/

I had a feeling this might be the case. I'm going to have one last try at searching for the card before giving up and re-buying Office. Thanks for the help anyway.

Thanks for the tip. I'll give this a try.