Cannot Ping myself

I am using Windows XP. I enter ipconfig. I see my IP address, sub and gateway address. I enter ping xxx.xxx.x.xxx (my IP address) and I am receiving request timed out. I can ping the gateway. I can ping all of the other PC’s on my network. When I try to connect to another PC, I cannot. Other PC’s can see me on the network, but cannot access me (it says to check with the system administrator for access privilages). I cannot see other PC’s on the network.