Fixing the Photosmart C4580 wireless printing issue
Finally managed to figure out that firewall issue with the Photosmart C4580. For some unknown reason, Bitdefender didn't list out connected networks in its firewall settings the first time I tried configuring it. Now that it does, setting the wireless network in question to 'Trust Local', or 'Full Trust' resolves the issue. All of the printer's functions become accessible to the computer.