UPnP can't figure it out...
If the router is UPnP-enabled [see related article], UPnP ends up basically being disabled. Since the entire subnet the student connected the router to is now on the same downstream (LAN) side of the gateway, all computers running Win2000 or XP (or other Windows OSes with UPnP added) will get UPnP messages from whichever Internet Gateway Devices (routers or IGDs) are connected to the LAN. Since routers aren't intended to have their LAN ports interconnected, UPnP wasn't designed to handle messages from multiple IGD's, and the result is unpredictable UPnP behavior.
In a simple experiment, I connected the LAN sides of two UPnP enabled routers (a Linksys BEFSX41 and D-Link DI-804) together and plugged a computer running WinXP Home into one of the router's LAN ports. As expected, the results were unpredictable with icons for each router appearing and disappearing in My Network Places. When icons for both routers were present, I was only able to reach the admin page for the router that leased the IP address to my computer.
On the other hand, the XP Network Connections window never showed more than one Internet Gateway. But the computer sometimes got confused and locked up when I attempted to show the IGD's properties, and other times connected properly to the IGD in the same subnet. The result is a problem for a UPnP-savvy person who is trying to use UPnP to configure their router, since a random DHCP renewal can assign them to another subnet from which they won't be able to access their router. Owners of UPnP-enabled routers might also have curious users accidently or purposely enable services in their router's firewall via the Internet Connection icon that appears in their System Tray or Network Connections window. But since the router WAN port isn't connected (in most cases), there will no harm done.