I have a Payne PA10JA060-G. I can hear a buzzing but fan is not turning. What do I do? I looked at the capacitor but it doesn't appear to be bulging. Not sure what to do? The humming I think should indicate something but not sure what.

Look at the contactor switch.

Look at the contactor switch.

I let it sit for awhile then tried again. I used a stick to get the fan moving. The air is not cooling. Can it be anything but the freon?

The "Freon" has zero to do with it. Everything in an AC is not "freon." You probably have a burned out fan motor, but you will need to use a meter to find out the trouble. You cannot fix AC units by guessing, it will take using a meter. Look at these: https://dl.dropboxusercontent.com/u/8010163/HVAC_Troubleshooting.pdf
https://dl.dropboxusercontent.com/u/8010163/How%20to%20use%20Test%20Equipment%20Service%20Manu al.pdf
https://dl.dropboxusercontent.com/u/8010163/AC%20Wiring%20Diagrams.zip

If you were successful in getting the fan to start and run by turning it with the stick, you have a bad fan start capacitor.

The fan has a run capacitor which is a capacitor in an aluminum casing. It can have a value of anywhere from 5 to 10 Mfds and a replacement should be exact or within 10%. (See: Understanding and Selecting Capacitors (http://www.ien.com/article/understanding-selecting-capacitors/171510)) You can also have an open start winding and have the same thing happen. If you disconnect the capacitor and it still has a charge then the start winding is open for sure, but you need to test it with a meter. If you wind up replacing the fan motor you also replace the capacitor with one matched to the motor. Look at these: https://dl.dropboxusercontent.com/u/8010163/How%20to%20use%20Test%20Equipment%20Service%20Manu al.pdf
https://dl.dropboxusercontent.com/u/8010163/AC%20Wiring%20Diagrams.zip