3) If you determined that it blows air and have now went outside to the AC condenser then the first thing we want to do is to verify that you have given the command to the system to cool. Make sure you are telling the Thermostat AUTO-COOL-68 degrees. I say 68 just to be sure you set it low enough for the system to come on. Wait 5. Minutes after giving this command. Some thermostats have a built in anti short cycle that wont allow it to turn the outside on if it has tried in the last 5 minutes. This is so that you dont ruin the outside by starting and stopping quickly over and over again. Once the 5 minutes is over (and believe me you want to use a timer) if the unit does not turn on then check the AC breaker. Cycle this breaker and then set another 5 minutes. What happened? If you hear the compressor running and the fan spinning then go to #4. If you hear and see the fan running but dont hear the distinct sound of the compressor OR you hear the compressor but dont see the fan motor OR you hear the system try to come on every 30 seconds or so (usually what you hear is a brief hmmmmm chhhkk) then you most likely have a bad Capacitor. You can turn the power off and open the compartment door and see what size you need. It will be written on the capacitor. It will say something like 60/5 or 45/7.5 or 30/10 or 55/7.5 etc. These numbers are important. They are the capacitor size. The biggest number is for the starting of the compressor and the lower number is for the fan motor. Search the internet about where to get one. I wrote an article about how much to pay for the most commonair conditioning and heating repairs and capacitor replacement is a common one.
4) So both the compressor and the fan motor are on. After running for 5 minutes put your hand on the fat copper line, it will usually be insulated. Just move the insulation and put your hand on it. It should feel like a cold beer. If it does not then the most likely problem is that you have low refridgerant. This is not something that you are allowed to repair by yourself. You need somebody licensed by the EPA to handle refridgerant.
5) On the off chance that putting a new capacitor in the unit does not start the fan motor but does start the compressor then you have a bad fan motor. The easiest way to determine this before even buying the capacitor is to feel the top of the motor. You can feel it just by touching the top of the cage that the motor is attached to. When the motor is bad it will be burning hot, like hot lava hot. You will feel the heat wafting off of the unit as you walk up to it. Replace this motor. Remember to get the right size, rpm, heat value, HP, voltage etc.