My outside motor stopped running yesterday and it was Humming. So of course I went to Mr. Google and it said it could be the capacitor and to try spinning the blades to see if it would run. I did that and it worked and my blades are currently spinning. But it still does not cool. I know I have to replace the capacitor but would the bad capacitor be affecting the unit not cooling as well?

Absolutely. There are two capacitors or a single "split" capacitor. One is for the fan motor and one is for the motor for the compressor. The hum you are hearing is actually the compressor motor, not the fan motor. You will need to replace the capacitor for both the motors. As I said they are usually a split capacitor. There will be two numbers on it (such as 5/35, 7.5/60, etc.). The smaller number goes to the fan side and the larger number goes to the compressor motor, labeled "HERM".

To test it do the following:

1. Turn the power to the unit off at the disconnect at the outside unit.
2. Discharge the capacitor by taking a screwdriver and touch it from the terminals to the metal casing of the condenser. (Capacitors can hold an electric charge for a very long time).
3. Take a Multi-meter and test each side of the capacitor (from the "C" to "Fan" terminals, and from the "C" to "HERM" terminals). The capacitance is measured in MicroFarads (MFD or uF). It should be within 5% of the value on the label/printed on the capacitor.

If it is bad, replace it. Be careful to use the same size capacitor (the capacitance has to be the same, but you can use a 330V or 440V pretty much interchangeably).