Оформил: DeeCo
Автор: http://www.swissdelphicenter.ch

{Static linking. }

 uses
   WinInet;

 {...}

 function IsConnectedToInternet: Boolean;
 var
   dwConnectionTypes: DWORD;
 begin
   dwConnectionTypes :=
     INTERNET_CONNECTION_MODEM +
     INTERNET_CONNECTION_LAN +
     INTERNET_CONNECTION_PROXY;
   Result := InternetGetConnectedState(@dwConnectionTypes, 0);
 end;

 procedure TForm1.Button1Click(Sender: TObject);
 begin
   if IsConnectedToInternet then
     ShowMessage('Connected.')
   else
     ShowMessage('Not Connected.')
 end;