I wasn't expecting that problem. It might be the case that only the shop who sold you the computer would know the Admin password and who's to say if they retined that info. At the very least they'll want to charge you £50 for out-of-warranty servicing/repair.
I searched and found this (try not to click on the adverts, trying to sell you products to fix this specific problem)
http://www.wikihow.com/Log-on-to-Windows-XP-Using-the-Default-Blank-Administrator-Password
It's self-explanatory enough but in the 'Tips' section are some technical details which are beyond my understanding and only after those are one or two caveats that might have been more usefully placed at the top of the page.
For instance, if you only had one "User account" on your PC, then it probably had administrator priviledges. So, when it asks for admin password, your regular logon password may have been what it wanted.
Errr, you did have a logon password, right? (that's another debate, save it for later)
One of the other caveats was about XP SP2 possibly behaving differently from the worked example and suggests selecting "Safe Mode with Networking".
Hope this helps.