You need to remove the "Laptop Admin" account and run Sysprep from the Administrator (pro) or Owner (home) account. Here's what you do:
XP Pro
1. Log out of your account
2. If you are at the welcome screen, press control+alt+del twice to display the gina.
3. At the gina, type in "Administrator" as the username, and whatever you set as the admin password for the password
4. When logged in, delete the other account, and then run Sysprep. When it reboots, it will ask you for new user account names.
XP Home
1. Create an account called "Owner"
2. Log off your account
3. At the welcome screen, log into "Owner"
4. Delete your other account and run Sysprep