Muideen,
Maybe try this step-by-step procedure if you haven't already:
1. Enter the command interpreter.
2. Ping the ethernet controller in the computer you're using. Ping 127.0.0.1
3. Ping your router.
..... a) Get the IP address of your router. Type ipconfig.
......... Note the IPv4 address and the Default Gateway address.
..... b) Ping your router using the default gateway IP address.
4. Ping the other computer.
..... a) Do the ipconfig on the other computer.
..... b) Ping that computer's IPv4 address.
You should be able to pinpoint where the problem is by the above.
I'm a novice at networking so if any of the above is incorrect, gurus please correct me.
Skyzoomer