On the machine experiencing the problem, in the Computer Name tab of the System Properties dialog (brought up from Control Panel | System), the “Network ID” and “Change” buttons were disabled (grayed out). A message at the bottom of the dialog indicated that the reason for this was that “networking is not installed or properly configured”.

I was able to fix the problem by removing and re-installing the machine’s Client for Microsoft Networks, as follows:

  • From the Control Panel, open Network Connections.
  • Right-click on my active Local Area Network connection and choose Properties.
  • In the Local Area Connection Properties dialog, select Client for Microsoft Networks, then click Uninstall. Close the dialog and reboot when prompted.
  • After rebooting, bring up the Local Area Connection Properties again.
  • Re-install the Client for Microsoft Networks by clicking the Install button, selecting Client from the Select Network Component Type dialog, then selecting Client for Microsoft Networks from the Select Network Client dialog. Click OK all the way back out, then reboot the machine once more when prompted.