I have a Dell Dimension 3100 desktop computer and had a similar problem two years ago when my hard drive crashed. I bought a replacement hard drive, but like you, my computer came with no back-up CDs, such as Windows XP.
I got my computer in December 2005 and it later annoyed me to discover that from January 2006 Dell started shipping their Dimensions with a full set of back-up discs (including Windows XP). Now, even though my Dimension was out of warranty by two years, I tried phoning, Dell only to be put through to an Indian call centre, and trying to explain the problem to them was like banging my head against a brick wall! I decided to write to Dell in Berkshire and explain the situation to them. The one thing I had in my favour was the fact that since buying the Dimension 3100, I'd also bought two laptops from them so I could use the old "long standing customer" line to my advantage. I sent the letter on the Monday and got a phone call from them on Tuesday and basically they couldn't apologise enough. They sent me the required CDs (free of charge, of course), which I received on Wednesday (and another set on Thursday!) and another courtesy call from Dell to make sure I'd received my discs ok. Within minutes my computer was up and running again, and has been working ok ever since.
It might be an idea to try writing to Dell yourself. It's a pity we're not allowed to PM each other on here, otherwise I would have been more than happy to let you have the spare set of discs that Dell sent me.