OK Here is the nature of the problem... IF you can ping all the other IP of the other systems and you are getting a reply (which is the assumtion from what you noted before) THen all the PC are on the network and are all talking to each other. You are thinking because you can not browse them in network neighborhood they are not on the network. This is misleading. When you browse you need a device which will allow you to see the NetBIOS name of the system on the network. Since you are not running WINS or DDNS (W2K AD DNS) on your network we are seeing anything. Try doing a search for the PC <START> <FIND> you know the drill.... place the IP address in the box when you search for the PC. You'll find it. You might also enter the PC Name and find it also but it is less likely...

IT has nothing todo with cabling or network or settings if you can PING you are on the network