Вот (раскопал где-то давно)

Вопрос: Internet - онлайн или офлайн (есть ли в данное время активное соединение с Интернетом)

Совет:
Данный пример покажет, есть ли в данное время активное соединение с Интернетом

Private Declare Function RasEnumConnections Lib "RasApi32.dll" Alias "RasEnumConnectionsA" (lpRasCon As Any, lpcb As Long, lpcConnections As Long) As Long
Private Declare Function RasGetConnectStatus Lib "RasApi32.dll" Alias "RasGetConnectStatusA" (ByVal hRasCon As Long, lpStatus As Any) As Long
Private Const RAS95_MaxEntryName = 256
Private Const RAS95_MaxDeviceType = 16
Private Const RAS95_MaxDeviceName = 32
Private Type RASCONN95
dwSize As Long
hRasCon As Long
szEntryName(RAS95_MaxEntryName) As Byte
szDeviceType(RAS95_MaxDeviceType) As Byte
szDeviceName(RAS95_MaxDeviceName) As Byte
End Type
Private Type RASCONNSTATUS95
dwSize As Long
RasConnState As Long
dwError As Long
szDeviceType(RAS95_MaxDeviceType) As Byte
szDeviceName(RAS95_MaxDeviceName) As Byte
End Type

Public Function IsConnected() As Boolean
Dim TRasCon(255) As RASCONN95
Dim lg As Long
Dim lpcon As Long
Dim RetVal As Long
Dim Tstatus As RASCONNSTATUS95
TRasCon(0).dwSize = 412
lg = 256 * TRasCon(0).dwSize
RetVal = RasEnumConnections(TRasCon(0), lg, lpcon)
Tstatus.dwSize = 160
RetVal = RasGetConnectStatus(TRasCon(0).hRasCon, Tstatus)
If Tstatus.RasConnState = &H2000 Then
IsConnected = True
Else
IsConnected = False
End If
End Function

Private Sub Form_Load()
'если есть соединение, то IsConnected() = True, иначе False
MsgBox IsConnected()
End Sub

еще как вариант пинговать какой-то узел
http://hiprog.com/index.php?option=com_content&task=view&id=251661563