D'Arbib
I've never tried it with a cordless keyboard but other than that if you're sure it is correctly enabled, I can't think of anything. I've looked round the Asus site & I can't spot any known issues with Logitech.
I think that I would start by plugging in a wired keyboard if you've got one lying around. If it works with that it might be worth checking out the Logitech site to see if there are any later drivers.
I'm at work at the moment but I'll check my Asus motherboard manuals tonight to see if that gives me any bright ideas.