Really weird stuff:
A one year old machine has two ethernet drivers (eth0 is internal, eth1 external). Was running RedHat 7.2. Now running RH8.0. Installed onto brand new disk. Disk is OK.
Now, this machine (say, named BAD) will ping some of its peers on both the external and internal networks just fine. However, it can not connect to server TTT (example name) on either the external or internal interface. To make things more difficult it can not ping the gateway either.
The only thing I turned up really odd is that server TTT had /proc/net/arp showing the IP for BAD for the internal network (and its MAC address) listed under the external network.
It looks as if the network driver (3Com -- for both interfaces) is confused and is mixing up which interface is which when communicating with some machines. Really odd part, it that it always say the wrong thing to the same machines and the correct stuff consistently to other machines.