Networking Problem

[Joel Hammer]

I conclude from your letter that the arp tables were incomplete and you fixed
them manually, yes?
Now, the next thing I would try is tcpdump.
For example:
On the linux workstation:
In one xterm run:
tcpdump -i eth0 -n 
and in another run:
ping theotherworkstation

If you have too much garbage with tcpdump, use 
tcpdump -i eth0 -n | grep -v "Expressions to delete"
Here is what I see when I ping between work stations:

192.168.0.2 > 192.168.0.6: icmp: echo request
192.168.0.6 > 192.168.0.2: icmp: echo reply   
You may see an arp request if the machine has to broadcast to get the
hardware address of the other machine.
This should give you an idea of what is going on. 
BTW, how are you trying to ping them, with their ip number or their names?
If by name, do you have a DNS or do you have them listed in /etc/hosts?
Joel