The control board.
The brain. Often blamed, less often guilty, and the fault light on it is free information.
The control board takes the low voltage calls from your thermostat and decides what actually happens: when the blower starts, how long it runs after the compressor stops, whether safety switches are satisfied, and in a gas system the entire ignition sequence.
Older equipment does this with relays and no board at all. Most equipment from the last few decades has one.
The fault light
Nearly every board has an LED that blinks a code, and the legend is usually printed on the inside of the access panel or on the board itself.
That light is free diagnostic information, and it is worth photographing before anybody touches anything. Count the flashes and the pauses. It will often name the circuit at fault, which saves real time.
Why it gets blamed
A board is the thing that reports other people’s problems. A float switch that has tripped, a pressure switch open, a flame sensor dirty, a thermostat miswired: all of those present as a system that will not run, and the board is where the evidence appears.
Boards are also comparatively expensive, which makes replacing one a tempting repair to propose. If you are quoted a board, it is fair to ask what measurement condemned it rather than what symptom suggested it.
When it genuinely fails
Surges, which is the common one in a monsoon climate. The power outage guide covers why restoration is harder on electronics than the outage was.
Heat, in an attic or a rooftop package unit, over years.
Corroded relays, which stick or chatter.
Rodents, which find the cabinet attractive and the wiring edible.
A failed board usually shows as no response at all, or a response that makes no sense: the blower running continuously, the compressor never energising with the thermostat clearly calling, or a code that persists after the thing it names has been ruled out.