Do you mean the icon in the system tray, 4 squares that change with the connection status?
If I click on mine, nothing happens. A double click opens the Diagnostics, but I only use the icon as a check that I'm online.
If you mean the desktop icon, a double click opens the connection dialogue on mine.
I usuall connect by clicking either the IE or Firefox icons on the taskbar, which opens the connection dialogue.
Does that help?