Well, From your explanation, It seems the Keyboard no longer functions once you restart, so if there is no fault with the Keyboard, then the fault must be in the Bios itself or try another USB port.
Can you get hold of another keyboard, Maybe a PS2 to see if the issue remains.
You could try a Bios update which is 1302, or try not setting a password to see if you are able to access your OS.
I am not aware of any special requirement for your Logitech G910, so it should work.
I am also unable to find your issue specific on the net.
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