Hello KozAKid and Welcome;
A quick, down and dirty way to check the unit is to remove the inspection panel outside and find the contactor. Keeping yourself in the clear, take a plastic handle of a screwdriver in your hand and use the other end to push on the center of the contactor. If the fan and compressor kick in you may have a bad electro-magnet in the contactor. Cut the power off, remove the contactor and take it to the A/C supply house for repair or replacement.
If the fan and compressor do not kick in, it is most likely a blown fuse. There should be a disconnect in arm's reach of the unit which, in some cases, has cartridge fuses in it. There are two ways to check them, 1. use a voltmeter to touch both sides of the Line, it should read 210v or more; now take the voltmeter and put it on top of one fuse and the bottom of the other, reverse it. This checks the fuses without one getting backfeed. 2. Take the fuses out of the box and use an ohmmeter from one end of the fuse to the other to see if there is continuity.
If the fuses check out and nothing is wrong with the contactor, and the two pole breaker is on in the main panel, cut the power at the main and procede.
Get inside the compressor housing, take the spring clip off the junction box on the compressor, disconnect the 3 wires. Use the ohmmeter from a ground on the compressor to each of the 3 connectors on the compressor, record the reading of each pole. One of them should have the same reading as the total of the other two poles. If that doesn't prove out, there is a short in the compressor and it needs a new one. However, if it is a short in the compressor the fan would run without the compressor running.
About 8 out of 10 A/C units I have serviced had a wire burned off in the outdoor unit, if that is the case cut the burned wire off, strip it , put a new end on it and reconnect it.
I realize I have written a book on this one and you may need to print it out to go through all the steps I have outlined. Start by looking for the burned off wire. Best wishes and let us know how it turned out.