예전에 김영대씨 홈피에서 받은건데...
확인해보세요...

var
data: TWSAData;
sock: TSocket;
addr: TSockAddrIn;
iaddr: TInAddr;
i    : Integer;
j,k : Integer;
begin
  ListBox1.Clear;
  j := StrToIntDef(Edit1.Text,1);
  k := StrToIntDef(Edit2.Text,1);
  for i := j to k do
  begin
  try
    if (WSAStartup($0101, data) = 0) then
    begin
      sock := socket(AF_INET, SOCK_STREAM, IPPROTO_TCP);
      if (sock <> INVALID_SOCKET) then
      begin
        // zero out the addr struct.
        FillChar(addr, SizeOf(TSockAddrIn), 0);
        FillChar(iaddr, SizeOf(TInAddr), 0);

        //fill in the internet address
        iaddr.S_addr := inet_addr('210.108.212.5');

        //fill in the rest of the address.
        addr.sin_family := PF_INET;
        addr.sin_port   := htons(i);
        addr.sin_addr   := iaddr;

       // try to connect, if it failes then the port is closed
       if (connect(sock, addr, SizeOf(TSockAddrIn)) = 0) then
       begin
         ListBox1.Items.Add('Port ' + IntToStr(i) + ' IS open');
       end else
       begin
         ListBox1.Items.Add('Port ' + IntToStr(i) + ' NOT open');
       end;
     end else
     begin
       ListBox1.Items.Add('There was an error creating the socket.');
     end;
   end
   else
   begin
     ListBox1.Items.Add('Failed to initialize winsock.');
   end;
   ListBox1.Refresh;
finally
   WSACleanup();
end;
end;

답변 감사드립니다.^^*
테스트 해보니까 되네여~~~

그런데 속도가 느린데.  netstat 처럼 빨리 열린 포트 검사하는 코드는 없을까여??
지금 하고 있는게 넘느려서여~~~
부탁드립니다.