If the camera is not detected, then you should check if the Drivers are installed properly for the camera. Go to Device Manager using Start > Run > Devmgmt.msc. Make sure that the camera is installed properly. If you see a yellow sign, right-click the item and choose Update Driver. Follow the instructions and then restart the browser and the computer, and it should work.
Additionally, reinstall the Facebook Video package and restart the browser then try calling again.