All Dell computers have a seven character Service Tag. The tag is usually a black sticker with white writing and can be found on the top, front edge of tower computers or the left, front of a desktop laying on its side. All-in-One computers have the tag on the back, near the bottom left. Laptop Service Tags can be found on the bottom.
Visit http://support.dell.com and enter the Service Tag. On the resulting page, go to the Warranty link and the original ship date along with the warranty expiration date will be displayed.