OEM Home Key: Warranty Covered Hardware Failure?

I decided to reinstall windows but (a tad stupidly), I didn't check first to see where my license key was... you see, it should be on the side of my case, but I swapped that over for an Antec P180. I copied it down onto a piece of paper, but unsurprisingly that piece of paper is nowhere to be found.I've used a code from another Dell machine in the house to get into XP, but obviously that's no use for getting it activated,and I keep being told my copy is not genuine (ie by Windows Update), which is rather irritating considering it clearly is. I was told to chase up Dell about the problem by the windows activation tool, but all of their support is locked down to two options... warranty covered hardware failure, or paid-for support.