1.
Firewall. If the computers have software firewalls, check their settings. If I remember correctly "ping" is part of the Internet Command Message Protocol (
ICMP). Ensure each firewall allows both the "incoming" ping and the "outgoing" response.
I not sure it's listed as "ping". Might be listed as
ICMP "echo request" and "echo response" messages. See the following Wikipedia article:
PING.
2.
Operating System. What operating systems and service pack levels are you working with?