After two days of tweaking switch settings, starting up the ARM software, going out to the living room and starting up the Rio, waiting for it to not boot, shutting it off, and going back to the computer, I've gotten my four(!) Rios booting from a Windows XP machine with Windows' firewall enabled, plugged into a Dell PowerConnect 3324 managed switch. Thanks to all the posts on the board for help.

To set up the switch, I had to set the ports the Rios were plugged into to 10mbit, half duplex, mdix on, autonegotiation off, and (this one was key) spanning-tree portfast. This last one is the Dell equivalent of "port fast" as described in this board post from iceweazel.

To get through Windows XP's firewall, I had to open up ports 67 (bootp), 12078 (http), 18678 (dunno), and 21075-21078 (ssdp, I think). I opened both TCP and UDP for all of them to finally get it to work.

This is all short-term (I intend on controlling all four from remote locations, as they're not really accessible, and just serving as digital amps), but I figured I'd post the details here in case anyone came looking in the future.