Athena is not dead. She's just blind. Or rather, I'm blind while using her. Turns out it's just the display that's not properly configured. First I reconfigured from scratch and recompiled the kernel using the liveCD, then I rebooted, and waited a bit.
I observed that the Ethernet jacks in the back both became active. I tried "ssh root@athena", but there was no address associated with that name. Makes sense, you can't resolve the IP address of a hostname if there are two of them (I had been using eth1 exclisively, but this last install, I switched to eth0 and eth1). So, I logged on to the router and checked the DHCP clients table. There were two entries for athena, so I opened two cygwin consoles and ssh'd to each of the addresses.
I had to clear the entries for the IP addresses on in my known_hosts file first, ssh doesn't let you log in to a host that doesn't have the same key that it remembers it having. So, I made it forget.
With that, I was in. I confirmed that nothing else was amiss, I logged in blind with athena's keyboard and checked who was logged in with "who", then I logged out, and checked again.
So, now I know that my custom kernel works. It just needs a working graphics driver. Or something.