The Javascript library is different from the .NET library, but the way they use the network is the same.
If, using wireshark, you don't see anything on the NIC while the RTD app loads and tries to connect, this, would make me think that there is some local application that is blocking the outgoing packets. Even if it wouldn't explain why everything works with push.lightstreamer.com.
Could you double check that there is no local firewall even? (Windows Firewall? Try to turn it off just in case).
At the same time, could you, through support@lightstreamer.com provide us some valid credentials that we can use to connect to your server through the RTD library, if possible?

Regards.