Ah-ha! I knew I could get there, I just didn't remember how. This page is very helpful, if you've almost but not quite forgotten everything you ever knew about DOS (and I used to be quite proficient, eons ago): http://publish.uwo.ca/~jkiernan/dosusing.htm.
I've run the command: "ipconfig/flushdns" successfully (according to DOS) and now I'm going to log off of the modem, restart the computer, go eat lunch, then come back and see what happens.