Hi Trouble2213,
I'm afraid that the loss of your Product Key is a problem as it is not on the disc itself anywhwere. The only other hope I can think to suggest is that you call Microsoft, explain your circumstances & ask them what they can suggest...?

But I don't like your chances, as when you install the OS, your next step is to input the product key, without which, your install can't progress, as I understand it...
Another member will be along soon who might have other thoughts on the above, but it's my belief this is where you stand.
I know it is possible to get Product Key codes from MS that keep you going for about a month or so,( like a 'demo' version'), allowing you to finish your immediate installation of the XP OS, but sooner or later, you will need to activate it, & unless you can find the correct PK, you may be unable to proceed past that month, or, have to pay out for it again to MS...

Please let us know how things work out, as a solution could help another user down the track...
Cheers,
Mike7