Sooo... now I feel silly.
I forgot the first lesson of error checking.
"Have you tried turning the device on and off again?"
I did not do that with the windows PC, and it was the windows PC that seems to have refused giving access to the pad (though it didn't have any problems with the phone).
Windows works in mysterious ways I guess, but problem solved.
Again, that's for the quick feedback, it put me on the right track.
