In order to check for an internet connection you need to use the Windows API function InternetGetConnectedState which returns either true or false.  You can also get the connection type from the dwFlags parameter.  In our example I will popup a dialog box but you can do what ever you deem necessary with the results according to your specific needs.

    'Declare the API function

    Private Declare Function InternetGetConnectedState Lib "wininet" _
        (ByRef dwFlags As Long, ByVal dwReserved As Long) As Long

    'Define possible connection types
    Private Enum ConnectStates
        LAN = &H2
        Modem = &H1
        Proxy = &H4
        Offline = &H20
        Configured = &H40
        RasInstalled = &H10
    End Enum

    Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
        Dim lng_dwFlags As Long
        Dim blnConnected As Boolean = (InternetGetConnectedState(lng_dwFlags, 0&) <> 0)
        Dim strMessage As String
        Dim ConnectionType As ConnectStates

        If blnConnected Then
            strMessage += "Computer is Connected" & ControlChars.NewLine

            'Display the connection flags
            strMessage += "Connection Flags: " & ControlChars.NewLine
            For Each connectiontype In _
                System.Enum.GetValues(GetType(ConnectStates))
                If (ConnectionType And lng_dwFlags) = ConnectionType Then
                    strMessage += "     " & ConnectionType.ToString() & ControlChars.NewLine
                End If
            Next
        End If

        MessageBox.Show(strMessage)
    End Sub

'This code does not verify that a connection is active just that the computer is currently configured for the internet.