How to check if a comparator is broken?
The long leg of the LED was attached to the corresponding output pin with a 1kohm resistor in between. The short leg of the LED was attached to ground but the comparator GND pin was not. I expected the LED to light up when I flipped the power switch.


Seems to me that you have connected the Anode to the output of the comparator and the cathode to the GND, that can not work for an open collector/ open drain output , the way this works is that you have to connect the positive supply to the load (LED and resistor) and then the output of the comparator will provide the ground (sink current) to the load (LED Cathode)