My furnace blower motor stopped operating with the AC turned on. The A/C condenser runs and my thermostat display shows the fan motor on but it is not, We recently lost power numerous times due to an electrical storm. The furnace blower motor fins and shaft turns freely and there is no humming coming from the capacitor when the system is running.

The blower relay might be defective causing the problem.

You really need to use a meter and check the blower motor power to see if it being supplied if not then you need to back track the power wires to see why no power is being supplied.

Sometimes I wonder if electrical storms kill capacitors... when I lived in phoneix we always were replaceing them after the monsoons. Might want to get that looked at.