You can see if simply removing and reseating the wireless card gets it to work again. If the connection manager software fails to turn on the wireless card (or get a Network Controller device to show up in the device manager), you can safely assume the wireless card has a problem. It is either because it is turned off by the connection manager software, or it has suffered a hardware failure. Your screen shot shows that no existing hardware needs drivers, which means the wireless card is not present at all. If only the wireless driver was missing, you would be seeing a device listed in the device manager as a Network Controller. This package provides the HP Connection Manager for the supported notebook models and operating systems.
See if installing the HP Connection Manager software and using that to turn on the wireless network adapter gets it to show up.
