Edits: Everything shows up as gigabit and full duplex on both the switch and the Supermicros. Flushing the 3com's cache...
Update: It's not the 3com. We've tried it with another managed 3com model, and with an unmanaged Netgear, and it's failing the same way - that is, these systems can see each other, but not other stuff on the LAN. We've done specific IP assignments, and tried DHCP - they can't connect to the DHCP server.
Now, these systems were working to other systems across an unmanaged Belkin switch. And they can talk to each other over anything. But they can't talk to other stuff over anything except when the Belkin was working (which isn't here to retest with). We've also of course swapped cables, swapped the use of the 2 NIC ports, tried it with the crossover between the systems disconnected - to see of that being there was confusing things for the other port. Connectivity stays broken.
Update 2: Just spoke with Supermicro's SuperServer support line. They have no idea what's wrong.