I set up the network that's already in place, with the correct name. I can access computers 3 and 4 fully. It recognizes computer 2 (laptop is computer 1 in this discussion), but won't access files on that computer, and vice-versa.
It didn't recognize computer 2 at all (and vice-versa) until I keyed in the IP number for #2 individually in Zone Alarm. The others picked up after I entered the IP range, which included the address for #2. I tried disabling Zone Alarm, but that didn't make a difference.
I'm still working via ethernet cable at this point, and #2 is the most important one for me to access, as it is my own main computer.