Normal users were unable to shut the teacher stations down (default Win2K Server policy).
I've adjusted this policy (called "Shut down the system"), which is found in Control Panel>Admin Tools>Local Security Settings>Local Policies>User Rights Assignment. The default setting is to allow only Power Users to shut the machine down. This has been changed to Everyone.

Another angle on this was that the shutdown button was disabled at the logon screen. This has been overridden in Group Policies thusly:

To enable the Shutdown button for Windows 2000 Server:
1. Start the Group Policy (Local) Microsoft Management Console (MMC) snap-in (run>gpedit.msc).
2. Double-click the following items to open them: Local Computer Policy, Computer Configuration, Windows Settings, Security Settings, Local Policies, Security Options.
3. Double-click Allow system to be shutdown without having to logon, and then change the local policy to Enabled.
4. Click OK.
The change takes effect when you restart the computer.