A little searching online and talking to people who know about these things, I found that it was probably the capacitor in the outdoor unit. The fan would run if I used a screwdriver to start it. Otherwise it would just sit there and hum with no fan running to cool the condenser. I took the back panel off the unit and exposed the guts.

Well, there's only one thing labeled capacitor.

I removed the wires after labeling them with tape. I also took these photos and a few others to remind myself of how it was attached, just in case. I learned this lesson the hard way early in life.
The capacitor was blown. See the bulge on the top at the front near the ring?

Unfortunately, I had to drive all over town to find one. Lowe's doesn't carry them, but a guy I work with recommended a place. I went to the electrical supply company. Nope. Try Goodman's. Well, those people are just a shop window and a warehouse. They offered to come out and fix it for the low, low price of $149, plus parts. The next place only had a 440VAC unit. Mine is a 370VAC. Ok, I'll try another HVAC repair company. Same thing, only 440VAC capacitors. Both told me I could use it, but I wanted the same part, not something else. I've learned those lessons early in life too.
The last place I went gave me the same story, you can use the 440VAC. That's why we only stock those. No one carried the 370VAC capacitors because they aren't as common. So why not just replace it with this one? It'll work. Well after being told this three times, I decided to throw caution to the wind and install it. It only cost $18, plus tax. It works. If only it were warm enough to turn the air on. It's 64 degrees.