broadcom netlink gigabit ethernet = wired (not wireless) network card. Are you browsing the internet using a network cable now on that machine? So you can download the driver (if I know which one)? Otherwise download on other machine, put driver on usb stick, plug it to machine with wireless problems and install.
so no wireless driver installed on that machine. 1 "other devices" in class "network controller". That's refering to a network device without a driver. It must be the wireless adapter driver.