Getting a new unit didn't help. I returned the original and received a replacement today, and it also will not work with the K780 or K400r or K400+. Three wireless keyboards and two 400 Minis and no combination of console, usb dongle port, or keyboard model works. Double checked my A500 mini and it just works right away. Shame this doesn't.
In fact, through all my experimenting, I'm finding that putting the Logitech dongle, or a wired keyboard, into Jack1 and the Joystick in Jack4 causes problems. I can use the joystick to select games, but then the stick stops working in the game. I can back out to home and the stick works again, but only for the carousel. This happens to both the 400 minis I currently have. Is there a problem with the USB in these systems?