From your answers it appears that you have something not set up correctly.
Since you say your time zone is GMT +01:00 I assume you are somewhere in Europe. If so I question why a time server half way round the world would give you better time than one based in Europe considering the latency over the net.
There should be no connection between the time setting and the ability to find the DNS-323 on the network unless you have blocked it with the router in some way.
Since you say you have had this problem for years I would do a very careful evaluation of your network setup, paying particular attention to how you router is setup - what time zone is it set for, for instance.
When you set the NTP server to one that apparently does not allow you to find the DNS-323 have you tried using a browser set to the DNS-323s IP e.g http://192.168.0.

or whatever it is?
Another thing you could try is to use netscan by SoftPerfect - it is free - to see if you can find the DNS-323 on your network. If that doesn't show it up then it appears you more likely have a network problem rather than a NAS problem.