Log on to the account you want to disable the internet access on then goto the control panel, network and sharing and then click on change adaptor settings, it`s in the list on the left. Then right click on the network connection you want to disable, choose disable and it`ll ask for the admin password, enter it and the network adaptor will be disabled. The only way it can then be re-enabled is by using the admin password.
You could also use a firewall to lock everything down. Set it to block all incoming and outgoing connections.