Duda verificando si tengo internet ?

Public Shared Function CheckForInternetConnection() As Boolean
Try
Using client = New WebClient()
Using stream = client.OpenRead("http://www.google.com")
Return True
End Using
End Using
Catch
Return False
End Try
End Function
Deberías comprobar la disponibilidad de tu adaptador, no la disponibilidad de un host (ya sea Google o cual sea)...

Esto lo he sacado de mi framework comercial ElektroKit:
Código
Imports System.Net.NetworkInformation
 
Namespace ElektroKit.Core.NET.Tools
 
    ''' ----------------------------------------------------------------------------------------------------
    ''' <summary>
    ''' Contains networking related utilities.
    ''' </summary>
    ''' ----------------------------------------------------------------------------------------------------
    Public NotInheritable Class NetworkUtil
 
        ''' ----------------------------------------------------------------------------------------------------
        ''' <summary>
        ''' Prevents a default instance of the <see cref="NetworkUtil"/> class from being created.
        ''' </summary>
        ''' ----------------------------------------------------------------------------------------------------
        <DebuggerNonUserCode>
        Private Sub New()
        End Sub
 
        ''' ----------------------------------------------------------------------------------------------------
        ''' <summary>
        ''' Gets a value indicating whether at least one of the current network adapters is capable of connecting to Internet.
        ''' </summary>
        ''' ----------------------------------------------------------------------------------------------------
        ''' <value>
        ''' <see langword="True"/> if at least one of the current network adapters is capable of connecting to Internet; 
        ''' otherwise, <see langword="False"/>.
        ''' </value>
        ''' ----------------------------------------------------------------------------------------------------
        Public Shared ReadOnly Property IsNetworkAvailable As Boolean
            <DebuggerStepThrough>
            Get
                Return NetworkUtil.GetNetworkAvailable()
            End Get
        End Property
 
        ''' ----------------------------------------------------------------------------------------------------
        ''' <summary>
        ''' Evaluate the online network adapters to determine if at least one of them is capable of connecting to Internet.
        ''' </summary>
        ''' ----------------------------------------------------------------------------------------------------
        ''' <returns>
        ''' <see langword="True"/> if at least one of the current network adapters is capable of connecting to Internet; 
        ''' otherwise, <see langword="False"/>.
        ''' </returns>
        ''' ----------------------------------------------------------------------------------------------------
        <DebuggerStepThrough>
        Private Shared Function GetNetworkAvailable() As Boolean
 
            ' Only recognizes changes related to Internet adapters.
            If NetworkInterface.GetIsNetworkAvailable() Then
 
                ' However, this will include all adapters.
                Dim interfaces As NetworkInterface() = NetworkInterface.GetAllNetworkInterfaces()
 
                For Each ni As NetworkInterface In interfaces
 
                    ' Filter so we see only Internet adapters.
                    If ni.OperationalStatus = OperationalStatus.Up Then
 
                        If (ni.NetworkInterfaceType <> NetworkInterfaceType.Tunnel) AndAlso
                           (ni.NetworkInterfaceType <> NetworkInterfaceType.Loopback) Then
 
                            Dim statistics As IPv4InterfaceStatistics = ni.GetIPv4Statistics()
 
                            ' All testing seems to prove that once an interface comes online
                            ' it has already accrued statistics for both received and sent...
                            If (statistics.BytesReceived > 0) AndAlso (statistics.BytesSent > 0) Then
                                Return True
                            End If
 
                        End If
 
                    End If
 
                Next ni
 
            End If
 
            Return False
 
        End Function
 
    End Class
 
End Namespace
Saludos.