"...Outside fan wont work but will run with a little push with a stick"
That is an indication of a dead RUN capacitor. The run capacitor is usually aluminum and either oval or cylindrical, about 3 to 5" tall. There can be 3 wires at the top labeled H, F and C. That capacitor will have a microfarad value on the side, something like 35/5 or 40/7.5. You need to buy an identical replacement as far as the microfarad value goes. The voltage can be equal to or greater than the voltage on your capacitor.
In addition to the run capacitor you may have a start capacitor. And from your description it sounds like you do. Since those start capacitors are only in the circuit briefly, you can get a generic replacement based on the size of your compressor. Post the make and model number and we should be able to help determine the size of the compressor. Any HVAC supply store (Johnstone, McCalls, Grainger) will have what you need.
Make sure you note VERY CAREFULLY the wiring before removing anything. Also be sure ALL power is off to the unit both at the 240 volt disconnect outside and the indoor furnace/air handler.