basicly you want to copy the settings from the working machine to the secound machine.
if you do ipconfig /all it will list the ip address as well as the dns servers and gateway.
Like snapshot has said it should be the same as the working machine.
if you go to network connections, right click the wireless connection and choose propieties you can highlight tcp/ip and click propities it will show all these options.
you could put in a static ip if you wanted, say 192.168.0.3 (if it's not being used) set the subnet mask to 255.255.255.0 and then the gateway to 192.168.0.1.
you might have to enter the dns server as well, but again just copy what the working machine has displayed.
let us know how you get on.
EDIT; sorry it took me so long to reply. internet went down last night at home. (Rubert Murdock - I love you!!)