Cannot ping computer

I have tried to setup a network using Windows XP Pro with 2 PCs, cable modem, integrated Intel Pro/100 VE adapter,and Linksys BEFSR81 router. For Basement PC, I can ping itself, the gateway, and the DNS server (everything is automatic assignments). The other computer, Bedroom, I can ping the first computer, the gateway, and DNS server. I cannot ping the computer itself. In various web help sites, I have not found what to do if ping 127.0.0.1 and / or ping 192.168.1.100 do not work. They just say try it and should see a reply and then move on to the next step without providing any insight what to do if the ping does not work. Any thoughts / suggestions? Thanks for your help.