Right click the taskbar then hit properties.
Go to notification area and make sure the network button is checked.
That will give you the 2 computers icon.
When you say blue ball are you talking the one with an A in it?
Thats the Avast AV icon.
No it has nothing to do with that particular anti virus software. I use Eset Nod. vista has, when turned on from the tray, two overlapping monitors appear in the tray next to the speaker icon. When the system is receiving internet a blue globe appears right next to the two monitors, indicating that the system has internet service. When the blue is missing, indicates you have no internet service. For some reason mine appears and disappears, but internet service continues to work either way.