Can you confirm that you have run Lightstreamer BB Demo on your local installation and in that case you have experienced problems only with old versions of BB?
Then you have tried to run the online demo at www.lightstreamer.com, but with connection issues?
Or is it the other way round?

Let's keep the cases separated for now.
Note that the demo midlet tries to connect to push.lightstreamer.com on port 8888.
Is it possible that firewall restrictions come into place in the second case?