This program uses the VB6 SP5 version of the Winsock control because that is the version I have on my machine. If you have VB4, remove the control and replace it with the VB4 version.

Note that this method seems to get confused if your machine is a network server. In particular if the machine is a personal Web server, the routine thinks you are connected to the network.

Private Sub Form_Load()
    If OnTheNet Then
        lblConnectInfo.Caption = "Connected"
    Else
        lblConnectInfo.Caption = "Not connected"
    End If
End Sub

Private Function OnTheNet() As Boolean
    Winsock1.Close
    Winsock1.Bind
    If Winsock1.LocalIP = "" Then
        OnTheNet = False
    Else
        OnTheNet = True
    End If
End Function