Yes, one of the machines whose disk I tried to map had the extra protocol. I think this screwed up the DHCP IP Table on the router. And maybe one of the computers had the wrong workgroup name.

Anyway, clearing the protocol, fixing the workgroup name and rebooting them all 2 or 3 times cleared it up. I'm happy to report that they are all working together nicely now. I can ping and map everything to everything, including any computer running the BART.
I plan on purchasing the BART CD in the very near future. I am moving to NYC in Feb and, hopefully, will be using it a lot there.