Logitech MX5000 not working properly

[Thorny]

[...]
> I have a Logitech MX5000. This is a bluetooth keyboard/mouse
combination
> with an usb bluetooth dongle. The keyboard has an LCD that shows when
> it's (dis)connected.
[...]
> The symptoms:
> 
> * Turn the computer on, with the dongle plugged in. * The keyboard
> becomes responsive after a few seconds, just in time to use it for
> "Press F1 to enter setup", "Press F8 to enter boot menu" --> typical
> BIOS messages. * After the usual hardware checks, I get the GRUB menu. I
> can use the keyboard.
> * I can use the keyboard during the init scripts. * I have automatic
> login. (I'm the only user) * The keyboard and the mouse do not work in
> Gnome. * There is a bluetooth icon in the top bar. * I unplug and replug
> the usb dongle. * Bluetooth icon disappears. * The keyboard and mouse
> work.
> * Bluetooth icon doesn't come back.
> 
[...]
> I would like to hear about further troubleshooting that I could do to
> investigate this problem.
> 

I don't really know anything about Bluetooth, and you've probably already
checked the logs, eh? Is there anything in the messages log that might be
relevant to the issue at the time you unplug and re-plug the dongle?