FWIW! When I first got my smart dock and tried to use my logitech k400. It did'nt work. So I had to re-pair it by plugging in the dongle to one of the usb ports on my computer and going about the whole process to pair it with the keyboard. Once that was done. I unplugged the dongle from the computer then plugged it back in the smart dock, and everything worked. So that may work for you. But if it doesn't, then I would replace the keyboard and or the dock.
Also for anyone wondering how to get the screen to turn off while its plugged into the dock. I use an app called Screen Standby. And if I remember correctly. It should work both unrooted and rooted. I also use Rotation Locker to manually change the screen orientation to landscape. These two combinations have worked great for me whenever I use my dock.
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