Compressor problem after brownout

When you say the compressor is not running, is it cold, or very hot?
If Hot remove power let it cool off then reconnect to power, listen carefully to see if compressor starts. If it does GREAT. If it does not you should hear a click after a few seconds. That is a safety device to stop power to the compressor, or it would destroy itself from drawing too much power from not turning. If this happens then the compressor is stuck. (this is as far as you can go without an AC man)
If it's cold, and has been plugged in for a while then either power is not reaching the compressor ( bad safety device mentioned above stuck open or burned out), or you have an open connection. This open connection could be outside, or inside the compressor. If inside, then compressor replacement is the only solution.
Another problem,if cold and it's a frost less unit, it could be the defrosting clock stuck on defrost. This would make the inside of unit warm because it turns on a defrosting heather. If this is you case then find the clock. usually positioned at front bottom behind the removable grill. It has a one way slotted fit. Use a wide flat screwdriver to slowly turn the dial to see if compressor starts. If it does great, but not done yet. After a while turn clock again slowly until the compressor stops, then wait (up to 30 minutes) to see if starts up again. If it does not clock needs replacement. I usually replace clock anyway at the first sign of problem, because chances are it will stop again. Best I can do without being there, hope it helps you.
Frank