When you install the 3 Mobile Broadband software, an entry is added in the Network Connections folder for a "Dial-up" connection. If you double click this, you will connect without having to use the Connection Manager, which may still show you as *NOT* connected, even though you are.
Additionally, if the Mobile Broadband is set as your default connection and in "Control Panel > Internet Options > Connections" you have selected either...
- Dial whenever a network connection is not present
- Always dial my default connection
...then as soon as you run a program that requires internet access (web browser, email etc), the Mobile Broadband will connect.