EPS8266 ESP-01: LED manipulation seems to interfere with serial communication
I would bet that the built-in LED pin is also the TX pin for the serial interface. 

Check here, LED Pin section: http://www.esp8266.com/wiki/doku.php?id=esp8266_gpio_pin_allocations


  LED Pin
  
  GPIO1, which is also TX, is wired to the blue LED on many devices.
  Note that the LED is active low (connected to Vcc and sinks through
  the chip to ground) so setting a logical value of 0 will light it up.
  Since GPIO1 is also the TX pin, you won't be able to blink the LED and
  perform Serial communications at thew same time unless you switch
  TX/RX pins.


This would be confirmed if the LED blinks when serial communication is active. 

If this is the case you would have to add your own LED on a different pin, or switch the RX/TX pins.