Did you do a factory reset and reconfiguration of the box?
I have already wasted too much time, so I have postponed it for the following days.
Thank you.
[UPDATE 1]
I have restored the factory defaults. The share works, only now the device name is "dlink-1919BB" instead of "DNS-323".

Easy search displayed, in the list of available drive letters, the previous mapped letter followed by the previous full path.

[UPDATE 2]
It still does not work the way it use to work. After I reboot the Windows XP machine I had to use, again, the EasySearch utility to remap the volume. The map does not transcend the sessions.
The power LED stays ON, although OFF is checked in interface.