Can you provide the Linksys router model info and firmware verison? Perhaps there is an option on the router to disable ICMP requests through the router. Can you give more details about the network topology, is it just some PC's and a Linksys router, or is there other hardware on it too, like a firewall perhaps?
Also, as Law requested above, can you provide us with the 'ipconfig / all' info from 2 of the PC's?
EDIT ALSO, when you said... "won't see anyother mac address"... what are you referring to? The router is only seeing the MAC address of one PC, or the PC is only getting packets from 1 MAC address?
If the you are saying the PC is getting packets from only 1 MAC address, this would be correct. that is because the MAC address is stripped off of the packet and replaced with each physical hop the packet takes... (except for hubs / repeators).
Example:
PC1 - packet leaves with MAC address of PC1, destined for IP address of PC 2.
Packet is recieved by switch or router, and the MAC address for PC1 is stipped from the packet. The packet is then sent towards PC2 with a SOURCE MAC address of the router / switch...