function GetIPReal: String;
var
  IP: TIdHTTP;
  Temporario: String;
  Endereco: String;
  X: Integer;
begin
  IP := TIdHTTP.Create(nil);
 
  try
    try
      with IP do
      begin
        Temporario := Get('http://checkip.dyndns.org');
        for X := 1 to Length(Temporario) do
          if (CharInSet(Temporario[X], ['0' .. '9', '.'])) then
            Endereco := Endereco + Temporario[X];
      end;
      Result := Trim(Endereco);
 
    except
      Result := 'ERRO AO RECUPERAR IP';
    end;
  finally
    IP.Free
  end;
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
  showmessage(GetIPReal);
end;