NetBeui is fine for small, single LAN networks. It is actually a very efficient LAN protocol, but it's not routable, which is why it isn't used for internetworks. It used to be better than IP or IPX for single-LAN MS workgroups, cos everything was based around NetBIOS names and broadcasts, but since Win2K (indeed NT generally), IP is the preferred MS protocol. And fair enough.
Curmudgeon,
Are you assigning both NTFS permissions and share-level access control? How are the shares set up - are you allowing everyone full control?
Are you mapping drives or browsing to the shares? Try mapping a drive and "connect using a different user name", then entering machineA\username as the user with your password in the dialog box. If you can't resolve machineA, you can always insert the IP address\username.
HTH
SD