OK, so it isn't anything I'm missing then. What I ended up doing at the time to see the printserver was going into the printer's properties and getting the forgotten address of the IP port out of that. Typing that IP into the browser address bar brought up the printserver's applet, which looks very similar to the router's (since it's also Linksys). Yes, it was being seen and apparently working as it should. The problem was the connection to the printer. The printserver's USB light was yellow, which I guess means it sees something, but it's not happy. Disconnecting the USB cable, waiting for the light to go out, then reconnecting made it green and happy. I'm thinking the issue there is that she has this old parallel-port printer, for which she got a USB conversion cable (which has to have active circuitry, I'm sure, maybe even an IC chip). Making everything happy there must be a bit more involved.
Thanks, Scott.