Air-conditioning unit on the outside won't come on - fan inside works fine. What would cause the air-conditioning unit not to come on. Thank you.

Check the fuses outside and the circuit breaker in the inside electric panel for the outside section..

After checking breakers, I would check Indoor unit float safety switch, sometimes installers
Use the float switch to shut all power to thermostat off and others shut down outside unit only.
If indoor unit is in closet or vertical in garage, look at bottom of unit where PVC pipes come out of unit. Look for wire coming off cap, pry open and check for water. Some have sight glass. If water is in either of these, you can use shop vac to clear drain from outside where
Water drains outside. Allso clear any water out of switch itself. If unit is in attic, look for water in emergency pan under unit. Next I would check refrigerant,Freon, Puron. Most newer
And better units are equipped w/low pressure cut out switches, Also look at t-stat wires to make sure there are no disconected wires, next I would check circuitboard. If breakers are not tripped and no water is backed up in drain you should call pro.

Ac fan will not kick in.When hit with screwdriver it began to kicked in

Are you talking about fuses inside of ac unit or main circuit?

I just had the same problem. I replaced the motor with no luck. It turned out to be a bad capacitor. If it is a dual capacitor, three prongs on top, it also starts the compressor. It is recommended to replace the capacitor anytime you replace a motor. I would try replacing the capacitor first. It is a lot cheaper that a new motor. If that does not fix the problem then you can get a motor. No harm, no foul. The slow start of the motor is a common symptom of a bad capacitor. The motor is not getting enough voltage. The capacitor increases the voltage like a transformer. It will boost it to almost 400 volts, depending on your unit.

Could also be your high pressure cutout. But it sounds like a weak capacitor