Welcome to the Community Forum and thanks for your post. I'm sorry to hear that you are experiencing a problem with your data connection via your Blackberry Passport. Has this been resolved for you since your post?
If you are still having a problem with this, please let me know if you are on a 3G or 4G tariff.
As you say the 3G or H symbol on the phone indicates it's getting a data connection, so things should be working!
Some aspects of Blackberry handsets rely on something called 'Blackberry services' which need to be provisioned on the network and won't be available unless the handset was purchased from us on a Blackberry tariff.
What handset did you have before and happens if you launch the browser on the device and try to load a webpage?