Central, "all-air" air-conditioning systems (or package systems) with a combined outdoor condenser/evaporator unit are often installed in North American residences, offices, and public buildings, but are difficult to retrofit (install in a building that was not designed to receive it) because of the bulky air ducts required. (Minisplit ductless systems are used in these situations.) Outside of North America, packaged systems are only used in limited applications involving large indoor space such as stadiums, theatres or exhibition halls.

I originally took off one star because of the SNAFU with getting the part ordered.  When Alberto called me on the phone he admitted the person had "gotten busy with other things" and apologized.  THAT was taking the high road and I was impressed by that.  Sadly, for reasons I won't guess at, Alberto has decided to take the low road in his comments and imply that they got the part as quickly as possible.  Well, we called at 2:30 so did someone spend six and a half hours finding the part??  That seems very doubtful.
Bigger is not necessarily better when it comes to HVAC systems, and smaller isn't always more efficient. If you have too small of a system, your system will be running constantly as it tries to keep up with the temperature. If you have too large of a system, it won't run long enough to keep up with the humidity. In order to handle both temperature and humidity efficiently, an HVAC system should run for around 30 minutes at a time. If your system is staying on too long or shutting off after only around 10 minutes, you are not getting efficient performance.
Natural ventilation is the ventilation of a building with outside air without using fans or other mechanical systems. It can be via operable windows, louvers, or trickle vents when spaces are small and the architecture permits. In more complex schemes, warm air is allowed to rise and flow out high building openings to the outside (stack effect), causing cool outside air to be drawn into low building openings. Natural ventilation schemes can use very little energy, but care must be taken to ensure comfort. In warm or humid climates, maintaining thermal comfort solely via natural ventilation might not be possible. Air conditioning systems are used, either as backups or supplements. Air-side economizers also use outside air to condition spaces, but do so using fans, ducts, dampers, and control systems to introduce and distribute cool outdoor air when appropriate.
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AC units and thermostats have built-in delay features when they're shut down and then repowered. The delay can be as long as 10 minutes. And, if you've subscribed to an energy-saving device from your local power utility, the unit can take even longer to reset. If you've installed the parts shown and reinstalled the disconnect block, repowered the circuit breaker, turned on the switch at the furnace, moved the thermostat to AC mode and lowered the temperature below the indoor temperature, and the unit doesn't fire up after 30 minutes, it's time to call a pro.
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.