It was the cable.

Get this, though: I got it set up so that both Navi and Toshiharu would appear in Network Neighborhood and "My Network Places" (on the laptop), and mapped all 3 of my 'doze drives on Navi to Toshiharu and vice versa. I decided to disconnect them and clear the "reconnect at login" option because it was looking for the buggers even when I didn't have the network cable plugged in, and then Navi disappeared from Toshiharu's "My Network Places", but both machines appeared in Network Neighborhood" on Navi.

I could still manually access files on my desktop from my laptop by using \\navi\\balthasar, \\navi\gaspar, and \\navi\melchior, and I could still map Navi's drives to Toshiharu, but Navi wouldn't show up in "My Network Places."

Then, for no apparent reason, the problem went away.