Ping을 자주 쓰기는 하는데, 때때로 Ping이 안먹히는 Network이 있습니다.
아래 함수가 더 정확하게 동작하더군요.

uses절에 WinInet 을 포함시키고 아래 함수를 실행시키십시요.

function CheckInet( psURL : String ) : Boolean;
var
  lhInet,
  lhUrl : HINTERNET;
begin
  lhInet := InternetOpen( 'jInet function by Pak jeong mo',
                          INTERNET_OPEN_TYPE_PRECONFIG,
                          nil,
                          nil,
                          0 );

  if Assigned( lhInet ) = TRUE then
  begin
      lhUrl := InternetOpenUrl( lhInet,
                                PChar( psURL ),
                                nil,
                                0,
                                INTERNET_FLAG_RELOAD,
                                0 );

      if Assigned( lhUrl ) = TRUE then
      begin
           Result := TRUE;
           InternetCloseHandle( lhUrl );
      end
      else
           Result := FALSE;

      InternetCloseHandle( lhInet );
  end;
end;