Prevent a users from loging into a domain but access domain resources

This is a follow up of a post earlier. I have about 12 new users set up with domain account. Their account is to allow them access the net. All internet users belong to a domain security group ‘allow net access’. I want these 12 users to be able to use one computer which is joined to the domain. They will use one local generic username and password. I do not want them to be able to log into the domain on that workstation
any leads?
Thanks