Macosxhints has a post that describes a script that will list the computer on a network. It uses the arp cache to get the list of computers on the network. It also will map the MAC Address to manufacturer for each device.
Since it uses the arp cache, the post has instructions on quickly access each machine on the network to populate the arp cache.
It looks like this script would help me find the computer that was causing the problems that I described in this post.
Update: I tried this on my Red Hat 9 computer, and the script didn't work.Â I am sure that I would just have to fix the paths for the commands that it uses.