I've got two in my system tray - you can display either or both (or not) by checking the box "Show icon in notification area when connected" in Status -> Properties -> General
One is for the local network - thats your PC talking to the ADSL modem and any other nodes on the network.
The other is for the "Internet Connection" as MS calls it and represents your PC actually making a connection to your ISP (via your local network and ADSL modem).
Not sure what's causing your problem though...