Did this system come with an actual full version XP CD; or with a dreaded (Dell in this case) recovery disk set?
If the latter then you may be able to get a replacement set from Dell; worth a phone call at least?
If the former.. then you may be able to a get legitimate copy (full version ) on eBay for a resonable sum. Also M$ "may" agree to sell you one for a wee sum (usually the cost of shipping?); but they will require some evidence you have a legit installation - a Certificate of Ownership number or similar?
If your installaton was an OEM (Dell on this occasion) and you once had the OEM (full version) CD... then not entirely sure how you get around that one. But again if Dell supplied the system they may replace the missing disk for a wee sum (postage again)?
Regardless of how you get the system running again - as soon as you can... make a set of recovery disks (as per a util supplied with many current sytems); or a restorable (and bootable) image set of disks.
Rereading your post I'm inclined to think you had a recovery set of disks from Dell at some stage; which means you ought to be able to get another set from them?
However... first I'd set about recovering data off the system as is? Boot with Knoppix or Ubuntu CD/DVD (Linux on disk). Use that OS on CD/DVD boot to access data etc and copy to optical media. Verify they can be accessed via another working system. After-which set about repairing/recovering the problem system.