Last evening, my A/C unit stopped working. I'd like to try to figure
out what died, how much it will cost to fix, and if I can do the
repairs myself.

We heard a sort of buzzing sound a few times, and when I looked out
the window, I noticed that the fan blades seemed to be turning slower
than usual. I went to the thermostat and turned off the A/C for a few
minutes. When I turned it back on, I could hear a short buzz sound at
the A/C unit, but the fan blades didn't move. The buzz sound would
repeat every 10 seconds or so, but the fan never moved.

I then turned off the A/C and flipped the breaker. I tried to spin the
fan blades with a screwdriver, and they turn freely. I checked the
service disconnect box outside the house, and all looks fine.

I'm thinking that either the fan motor died, or the compressor is
dead, or both. Any thoughts?