My linuxbox provides dhcp service and shares its internet connection with the other 2 computers in my home - so it's got two network cards (one connected to my home network, the other to the internet).

When I try to ping the other computers from this workhorse of a computer, I get "Destination Host Unreachable" errors, but I can successfully ping outside hosts (like www.yahoo.com). Is ping using only one of my NICs (the one connected to the internet)?

The other 2 computers in my home network can ping each other, but get "Destination Host Unreachable" errors when they try to ping the server. Plus, these computers successfully get IP addresses from the dhcp server (so they apparently can talk to it, yet they can't ping it...)

Can you provide us with the output of ifconfig? It's most likely a simple network mis-config. And maybe your dhcp server config.

mlp

Please post the IP addresses of each card and the masks and gateway and DNS settings in your network.
You have a routing issue .. but can't be helped without this information

To display your network cards' configuration, type: ifconfig
To display your routing table, type: route -n

Also, when you ping, are you using hostnames (mycomputer.pvt) or an IP (192.168.1.2) ?