My electricity went off, and then back on twice today, and now neither the compressor nor the inside fan will turn on-even with the fan switch in the "on" position. I've checked the breakers and changed the batteries in my thermostat. I do not see a reset button or switch on the outside unit.

Not knowing what model or if you have electric or gas furnace,, I would ask if it has a circuit board ? And does it have a plug-in automotive type 3 A fuse in it,if so check it for being bad

It was the fuse all right. An easy fix.
Thanks, wmproop!

Great, glad to help