It's possible that the wireless connection on the other PC may have been firewalled when the Network Setup Wizard was run - if that's the case it may not be visible on the network or others on the same network may not be able to initiate communication with it. Check the wireless adapter's settings and make sure that if it is firewalled that file and printer sharing is enabled.
Or try running the wizard again and make sure to select the option to connect through another device and not directly to the internet, it will also prompt you if that PC also has a wired connection - check the box to ignore disconnected hardware and continue the wizard.
Another possibility is that the wireless adapter may not be correctly obtaining the IP address from the router or access point. To find out about this, right-click the wireless adapter's icon in the system tray (the lower right corner where the clock is) and click Status. In the status window, click the Support tab. If the address comes up as a 169.254.xxx.xxx address, that's the problem - make sure it's set to obtain the IP address automatically, I also have mine set up to use a backup static IP if for some reason it can't get the IP automatically
I know this is a lot to try but wanted to make sure I didn't overlook anything - good luck....