Hello,
Make sure that you’re not using the same IP address – How does your routing table look in the wireless router? And as for the wireless router, make sure you are using WEP and turn off the SSID.
Also – if you can, try to recreate the problem – then disconnect one of the other computers from the network – the results may help in finding a solution.
Hope that helps!
Also – Make sure that your computers are using a non-routable IP address, such as 192.168.10.x or 10.10.10.x. Also – any computer will respond to a ping unless there is some type of firewall in place (such as XP’s, etc)