You should be able to make a rule to allow XNA through the firewall rather than switching it off completely. I though the XNA installer gave you an option to do this but I can't be sure.
To ping the other computers you need to know the machine name or IP address. You run the windows command prompt and type in ping Machine-Name (ie "ping My-PC" or "ping My-Laptop"). Alternatively you can use the IP address of the machines to ping them (ie "ping xx.xx.xxx.xxx"). To get the IP address of a machine, run the command prompt on it and type "ipconfig", the IP of the machine you use is the "IPv4 Address"