I had some of the same problems when I had to administer a school network. The students would move the whole computer and end up breaking the NIC, port, or cable.
Prevent the computer from being moved.
Bolt it down to the table.
Tie-wrap the cables to the table.
I think that Network Access Quarantine Control is also a very good, if you have the money for that type of option.
You could also increase the port timeout. On Cisco switches there is a setting to prevent just that moving from port to port to port. Increase the setting, I think the default is 5 minutes.
It is called Port Hopping and it is configurable on a Cisco 2950 switch.
