Unfortunately the circuit in your garage won't provide enough power to use the A/C, particularly if using any length of extension cord. The brown out of power before the circuit tripped may have damaged the compressor start capacitor in the unit, or the compressor it's self.
Can you post the make and model info for the A/C, may be a member who has had to replace one of these can walk you through the testing.
99DSDP 3884, Freightliner, XC, CAT 3126B, 300 HP /ALLISON 3060
2000 Caravan toad, Remco & Blue Ox.