I have two computers. One computer as windows XP and the another one as Mandrake 9.2 on it. Both computers are using the some router.
On my Linux Computer:
I ping the router and it pings (ping 111.111.0.1) no lost packets
I ping my Linux computer and it pings (ping 111.111.0.2) no lost packets
I ping my windows computer and it pings (ping 111.111.0.3) no lost packets

On my windows computer:
I ping the router and it ping (ping 111.111.0.1) no lost packets
I ping my windows computer and it pings (ping 111.111.0.3) no lost packets

When I try to ping my Linux computer it times out. Is there a security setting that I need to set the let my Linux computer to me pinged and seen by my windows computer? I have turned off the firewall on the Linux.

if the firewall is out then only 1 of 2 reasoons exist i think
1) windwos is stupid and not pinging right, or just ignoring linux alltogether
2) your linux computer was set up to not respond to pings, i know u can turn off ping in the /proc sysem, but i 4get what file it was

edit: ok ig ot bored, and been looking thru the /proc FS

can u tell me what the output of this comand is?
less /proc/sys/net/ipv4/icmp_echo_ignore_all

I would check your iptables file and see if it has been configured to drop ICMP requests. You might also try pinging it from the local treminal to see the reply you get. That may aid in your troubleshooting.