A – both the same OS? If it is XP are both same patch level? And most important if both xp and both sp2 are both set to pass ICMP thru the firewall?
B – Seriously if you can ping ‘A’ from ‘B’, but not the other way then it has to something blocking the packets? XP firewall does NOT allow ping by default.
C – Clarify your layout if this does not help.