Just ran into the same problem (I think) with a Logitech K780. The UI said it is paired, but the keyboard did not work. What fixed the problem: Running bluetoothctl and then switching once to unifying receiver and then back to bluetooth (as a replacement for turning bluetooth off+on at the keyboard, which doesn't have a switch).
My system is Xenial on HP Elitebook 820. Bluetooth chip: BCM20702A. Kernel 4.4.0-62-generic.
Just ran into the same problem (I think) with a Logitech K780. The UI said it is paired, but the keyboard did not work. What fixed the problem: Running bluetoothctl and then switching once to unifying receiver and then back to bluetooth (as a replacement for turning bluetooth off+on at the keyboard, which doesn't have a switch).
My system is Xenial on HP Elitebook 820. Bluetooth chip: BCM20702A. Kernel 4.4.0-62-generic.