Ok, update.
I just thought that I still have a Windows tablet laying around here, so I took it from the shelf and installed a second Directory Listing in CentreWare, especially for this tablet. I set it up EXACTLY the same as my desktop (with the exception of the IP address of course).
And what do you know? IT WORKS!
So the problem has to be with my PC somewhere. Something is preventing the 6505 from calling into my Desktop. You don't suppose Bitdefender is responsible for this ? I don't think so because it's only an anti-virus and not a total security package, but I've known problems before with NOD32 and my 6505 (albeit of a different kind), so I would not be surprised.
Hmmmmm....
Edit : I just tried uninstalling Bitdefender, but that didn't make any difference, so it seems Bitdefender is not at fault here...
I also tried copying a file from the tablet to the shared folder on my desktop, and that worked instantly and without a problem. So it seems the tablet can access the share of my desktop, but the 6505 can't. Now I'm very confused...