Did you see only one occurrence of the client-side stack trace for all the attempts shown in the Server log?

It seems that the client does not even receive session data,
although the Server receives the requests for opening a new Session.
So, it's like the client can't get the answer back.

As you say that the web client works, can you check if the web client resorts to smart polling?
Alternatively, you could try forcing POLLING mode in your .NET client and see what happens.
If smart polling works, then consider that in the forthcoming release of Lightstreamer we will add the Stream-sense feature also to the .NET client library, hence you will not need to force POLLING mode to overcome the case.