All of the computers on my four-computer network have the VIA MVP3 chipset. I have had problems with that chipset, Windows 98 (not 95), and IRQ conflicts with network adapters when the VIA IRQ routing driver was not installed, but have not seen it for awhile. I have D-Link DFE-530+ NICs (http://duxcw.com/digest/Reviews/Network/dlink/dfe530txplus.htm) in two of the computers and they use the Realtek RTL8139A chip. I don’t see how either can be a factor if you can browse the bad computers from the good ones. Looking back through the posts, I see that you tried several protocols. Did you try installing NetBEUI on all of the computers? Obviously, the computers must have a common protocol installed to communicate.
It appears to a Browse Master Problem. In Start, Setting, Control Panel, Network, File and printer sharing for Microsoft networks, Properties, try disabling the Browse Masters on all machines, shutting them down and power off. Pick one computer that is on the most and has the most recent version Windows (NT or 2000 Server would be the best choice if one is on the network) and enable the Browse Master. Bring all of the other computers back up and wait up to 45 minutes for them to become established with the new Browse Master. If that fixes the problem, you may want to set some of the other Browse Masers to automatic for backups when the Browse Master is off. Larry