Peer to Peer Networking Problem

I have 12 computers using Windows XP Pro, SP1, and they are networked using peer to peer. All computers are mapped to each other local hard drives. All computers can talk to each other, except two particular computers. These 2 problem computers can access to all other computer except each other. I am not able to ping each other, yet I replaced one problem computer with a laptop using exact same CAT-5 cable, and this laptop was able to ping other problem computer.

I checked for conflict in IP address and MAC address. IP addressing are automatically assigned. The Linksys 4 ports Router is the DCHP server.

What are the possible cause(s) of two particular computer not able to connect each other.?