AC Capacitor Troubleshooting

I have a Janitrol outdoor unit. Noticed the air coming out of the vents was not blowing but not cool. I went outside, and the condenser fan is not running. I gently prodded it with a stick and it started up and ran, but the air coming out of the vents is still not cooler. My discharge and suction lines both feel room temperature to the touch.

Is it possible I burned up the compressor by running it without the condenser fan?

Research seems to point me to the the capacitor causing everything. How does one check this?

Any other suggestions?

Thanks