You have to assign ownership of the files to the individual users. Administrators have access to all files on an XP machine. Regular users have access to files they are explicitly allowed and files that they "own." When you deleted the users in AD, you basically erased the SSID for the users. Windows defines file permissions and ownership based on SSID, and translates that ID to the human readable information stored in Active Directory.
To assign permission of the files to the user, right click on the folder and click Properties, then security, then advanced. Click the Owner tab and then Edit. Click Other Users or groups and enter the name of the user. Put a check mark in "Replace owner on subcontainers and objects. Hit OK on everything until you're out of the dialogue boxes.