Ok, most OEM (that is, manufacturer branded, like Dell) install discs are going to install with a product key already entered.

If this is the case, you could attempt to change the product key:
Easily Change Product Key with Windows Product Key Update Tool Free Download » My Digital Life

The product key for you copy of XP is on a sticker on the bottom of your laptop.

If that does work, you could track down a non-OEM version the Windows install disc, then use the original product key from your laptop. You'll need to head to the Dell support site afterward and download drivers for things like video, chipset, and possibly sound. Looking up your Dell service tag number (should also be on your laptop somewhere) will get you to a page that has all the correct drivers for your laptop)
Note, I am not advocating piracy in any way. Joshua has the original product key to his XP installation, the physical media ought not matter.

As a final solution, since this is an older laptop, probably not capable of running Vista or 7, why not put a modern operating system on it, like Ubuntu?
(Ubuntu Home Page | Ubuntu) It's free and easy to install.

--Sean