Reinstalling xp with original product key and borrowed disc

Hello, I might be missing something really stupid by saying this but I can’t find a situation on the existing posts the same as mine. Basically I have lost my xp installer disc. the computer came with xp installed and my product key is stuck to the case, so I have a legit key. I borrowed an installer disc but it said the key was incorrect. I phoned dell who sere useless. They said I would need to buy a new disc. This seems pretty unfair.How can the viewkeyxp program help (if at all)? I used the key on the back of the disc in haste and I can’t activate this so I’m totally stuck.
Any ideas?
Cheers