No. But, if you call microsoft, and wait long enough to speak with a help tech, they will tell you to borrow a disk (anything after 95) from a friend. XP doesn't care if was actually ever installed or not, it just needs to read 1 measley little file (which in your case it is getting from the install on the 20 gig HDD), and then it will let you move on.
The problem with what you are doing, is you have multiple installs of the same OS. This will get you by, but it is a little untidy, and severely frustrating. As well as very confusing. I would just find someone with an old 98 or 98se disk that will either let you borrow or have it.
My computer specs? Nothing a little Windex and a paper towel won't take care of.