When your home's central air conditioning unit fails to work, or it switches on but doesn't cool the home, you may not need to replace the unit just yet. In some cases, it can be simple problems with the unit that cause it to shut down or fail to cool your home. Note a few of those simple problems here, so you can at least try these before calling a repairperson or starting to shop for a new air conditioner altogether.
The air conditioner will only come on when it receives commands from the thermostat; if the thermostat is faulty, the air conditioner won't switch on even if the compressor itself is in good repair. If your home has a digital thermostat and the front panel is blank, or the numbers are flashing, the thermostat may simply need new batteries. If the battery compartment is not in front of the panel, you can usually pop the thermostat out of position very easily, and find the battery compartment.
If the batteries are fine, turn off the circuit and then pull the thermostat away from the wall, and check the wiring behind the panel. Are there wires in the thermostat that are not connected to wires in the wall? If you're sure the power is disconnected, twist those wires together and then make sure they're tucked safely into the wall, so the front panel won't crimp them. Restore the power and note if this addresses the issue.
No cool air
If the air conditioner engages but the home doesn't get cool, check the furnace filter. If it's very old and dusty, this can warm up the air before it reaches the ductwork of the home. You might also use a flashlight to look into the home's ducts and note if they're very dusty and dirty; this can also make air warm as it passes through those ducts. Change the filter and have the ducts cleaned to restore cool air to the space.
You might also inspect the compressor; if it's covered in leaves and debris, or anything is blocking the grills, this can mean the unit doesn't have proper air circulation. In turn, it can't work to compress refrigerant and create cool air. Look inside the compressor; usually the top opens by removing a few simple screws. Note if the fan is especially dirty or if there is any type of debris inside the compressor. Give the piece a thorough cleaning and remove anything that is blocking it, and this may allow it to create cool air again.