Capacitors -- Capacitors help your HVAC motor start from a standstill. Over time they can weaken. As they weaken, they cause the motor to run hotter. This can shorten the life expectancy of your motor. Once a capacitor fails, the whole motor will stop working. You usually won't notice that a capacitor has weakened until your motor stops turning on.
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If you hear clicking that is followed by a hum or buzz, you’re probably hearing the fan motor attempting to start without the boost it needs from the capacitor. You can almost always conclude that the capacitor has failed. Sometimes you can get the compressor fan spinning (clockwise) by pushing it with a thin stick or long screwdriver poked through the grille. But the chances are good that this might work for one cycle, but the capacitor will fail next time the AC goes on. It’s best to replace the capacitor.
If the condenser coils are clogged, the compressor can overheat and shut down. You'll experience intermittent periods of minimal cooling, followed by no cooling. Even if you're “sure” the condenser coils are clean, clean them again. Turn off the power. Flip the air conditioning service and furnace circuit breakers in your main electrical panel to the “Off” position. Next, turn off the power switch right at the furnace or air handler. Then yank the disconnect block (Photo 1) and clean the condenser coils (Photo 2). If the air conditioning service still doesn't work properly after you've cleaned the condenser coils, installed a new filter and opened all the supply vents, proceed with the following repairs. Your AC won't work fully unless you do this.

If your AC doesn’t turn off when room temperature reaches the temperature set on the thermostat, the problem is generally occurring either at the thermostat or in the electrical system that runs the outside condensing unit. You can use the AC’s circuit breaker to shut off the unit, but that should not be a permanent solution—circuit breakers are not designed to be used like light switches.

All modern air conditioning systems, even small window package units, are equipped with internal air filters. These are generally of a lightweight gauze-like material, and must be replaced or washed as conditions warrant. For example, a building in a high dust environment, or a home with furry pets, will need to have the filters changed more often than buildings without these dirt loads. Failure to replace these filters as needed will contribute to a lower heat exchange rate, resulting in wasted energy, shortened equipment life, and higher energy bills; low air flow can result in iced-over evaporator coils, which can completely stop air flow. Additionally, very dirty or plugged filters can cause overheating during a heating cycle, and can result in damage to the system or even fire.
Air conditioners can create a lot of water because they remove moisture from the air. To get rid of this, they have a [usually plastic] drain pipe that comes out of the side of the air handler. Over time, algae can block this pipe and, when it does, the AC won’t work. In fact, some condensate drains have a float switch that won’t let the AC run if water backs-up. Water can also puddle around the unit or flood the area. To deal with condensate problems, please see Air Conditioner Leaks Water, below.