Originally posted by Martin:

It is odd you get disco'd if steam goes down.. or do you literally mean your isp? Could try running steam in offline mode.. see if you can get it to connect to lan.. if it doesn't.. you'll need steam to be online.

It was literally the ISP. Steam was still up because I could get my server running by tethering it to my phone, I just couldn't get five computers tethered to my phone. I tried running the server in offline mode through the steam interface (even though the server logs in anonymously) but it still failed with that same error. I also tried running my local game in offline mode but we couldn't figure out how to connect - my game doesn't show up on the LAN and using my IP address didn't seem to produce any results. Good suggestion though.