Can you explain your thought process on the other items? I will explain mine:
If there was a problem in another area of the A/C system, I would figure the A/C light would turn on, but the system simply wouldn't work. Also, the item is rather easy to change and not expensive, so that was my logic to start there.
Now as far as the a/c compressor having power. I don't know that, don't know where to check, but do have a voltage meter. The freon should be full since I filled it last summer and has been working all year up to now.