As far as I remember when we fixed this a while back and the issue was that you had your LED installed backwards. Additionally this circuit was a passive circuit that wasn’t technically controlled by the Arduino.
For anyone else who might be encountering similar problems, I recommend first eliminating the push buttons and trying a super simple circuit with just the Resistor, and LED. From experience debugging this setup you will want to check polarity of your LED since it only works when it is facing a particular direction, and you will want to check your resistor value (http://resistor.cherryjourney.pt/) that is a nice resistor calculator. Make sure your resistance is between 100 and 1000 ohms, and more and you won’t see the light, any less and you will get a nice pop if you are lucky before your LED is no more.