Time for our annual home repair SNAFU!!! HVAC this time...(FIXED! Now I'm cold!)

I am a AC tech.
IF the thermostat is set for cool, there should be 24 VAC across the contactor coil terminals on the side of the contactor and it should be pulled in. With it pulled in, there should be 240 VAC on both the line side and load side of the contactor. With 240 VAC on the load side and the fan is not turning, it could be the cap or the fan motor itself.
I wouldn't let it stay like that for very long as the compressor will overheat without air moving.
We have meters that allow us to check capacitors to see if they're still good.
We've seen rusty ones like that which were just fine. If it's swollen or leaking, it's bad.
We've seen it all on outside units: snakes, mice, rats, lizards, etc.
Based on the info you posted, I suspect a bad cap as well.
FYI...Not always, but usually when caps go bad, the motor or compressor is not far behind.