Well to be precise this is the situation. I recently moved to another place bought a WIFI card and connected to the router withot problems.
Before I moved I connected to a router in my previous place via wired LAN. In that situation I couldn't get my PC to share folders with other "anonymous" users. So what I did was, I created the same useraccounts on both PC's which worked. However it cluttered my startup screen, but I could live with that. I never found out what the problem exactly was. Maybe it had something to do with the router.
So When I moved (and connected to the new wireless router via my new wireless WIFI card) I didn't un-share and then re-share my folders and printers. So that was the point when I posted this message. Between posts I coincedentally un-shared & re-shared a folder. Suddenly my PC was accessable via another PC connected to the router.
Moral of the story: start analyzing from the beginning in a new (networking) situation. People say the world is complicated, but sometimes it are just the simple things that make the difference.
Hope others can make use of my "mishap"

. I'm just glad everything works now. Just wondering why I had the problem in my old "wired" situation in the first place. I can't imagine it being a hardware problem (in the area NIC-ROUTER-NIC), since the user-accounts made it able to share folders when user-accounts where set-up synchronised on both PC's. But maybe I'm wrong.
PiC