In addition to the information below, see these two articles for the general care and maintenance of your air conditioner: Preparing Your Air Conditioner for Summer and How to Replace Furnace & AC Filters. Most noteworthy, you should replace the filters at least twice a year, before the heating and cooling seasons. For information on furnace problems, please see Furnace Not Working.
Because an air conditioner moves heat between the indoor coil and the outdoor coil, both must be kept clean. This means that, in addition to replacing the air filter at the evaporator coil, it is also necessary to regularly clean the condenser coil. Failure to keep the condenser clean will eventually result in harm to the compressor, because the condenser coil is responsible for discharging both the indoor heat (as picked up by the evaporator) and the heat generated by the electric motor driving the compressor.
Whether or not central air adds value to your home depends on your location. You probably won't recoup the entire cost for the installation, as it is an expensive project that isn't as flashy as something like a new deck. But this invisible upgrade can help you sell your home if you live in a hot climate. And many buyers are willing to pay a bit more for a working AC.
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.