OK, guys, thanks to those who encouraged me to look further.

Again, what was happening before was that the fan was running, but the
compressor was not running.

I turned off the thermostat altogether, for several days, due to cool
weather. Today, the weather was warm enough to try looking into my AC
again.

I turned the thermostat to COOL and nothing at all is happening. The
furnace fan is not blowing and the outside compressor and fan are not
running at all.

This is a change from 4 days ago, when at least something was running,
now nothing is running.

I spent some time today investigating this. This is what I found:

*) There is 120 volts coming into the furnace from the circuit breaker

*) There is 120 volts on the input of the 24 VAC transformer

*) There is no 24 VAC on the output of the transformer, the output is
0 volts AC.

*) The secondary (low voltage) winding has resistance appx. 1 ohm

*) The primary (high voltage) winding has infinite resistance, in
other words it is broken.

So, on its face the answer is that my air conditioner is not working
because the control transformer is not functioning. It should be easy
to replace.

What I am not sure is why it failed. Did it happen simply due to age,
or there was perhaps overdraw of current or a short in the 24v system
that caused it to fail? Any thoughts on this?

I can easily find a 120-24v transformer, but I am not sure if I found
the root cause or not.

i