You have power at the outdoor unit. I have found that about 8 out of 10 units with the problem you described have a wire burned off somewhere.
Turn the power off outside (there should be a disconnect switch there by it), open the unit up and see if you can find a wire burned off the compressor. To get to the compressor connection you will have to remove a spring clip and take the plastic cover off. If a burned wire is your problem, you can cut the burned part off, strip about 1/2" of the wire, put a new end on it and hook it back up. Let us know how it goes, I feel for you in this heat.