Your capacitor might have gotten damaged during the storm. The condenser is connected to the house via an electrical box called a quick disconnect I call it yank out. It is a quick way to kill power to the unit.
Quick Disconnect Power box for condenser unit
Note: this is not the breaker to the unit. That would be in the main panel by the meter. People always assume this is the only safety. It is put there by law to kill the power to the unit for service personel. Pull out the connection to kill the power before checking the unit. The first thing to look for is a swollen capacitor


. If it swells it fails and the unit don't function too well. The next thing to look for is contactor problems. Their are small wires coming from the inside control panel that power up the 24 volt coil that yanks down the contactor.
24 volt 2 pole 30 amp contactor with cover
That coil might be bad. If it has no continuity(open) it is in need of replacement. Pictured above (white) to the right is one side of the coil, on this model the other small wire goes on the other side. So check each side for continuity (notice one side has a double spade and is a pisser to the novice. A critter could get between the contacts and fry them as well. Look on the compressor for burnt wires and loose connections (very common). The fan motor should be very easy to turn so if it is stiff then it probably is in need of lubrication. The standard oil in the HVAC world is Zoomoil.