which one of your circuits was still powered?

I think it was the last one in line in the house - the bathrooms. My landscape low voltage lights were still on also.

I should also mention that yesterday it was hot, over 100+, and the AC ran day and night. The AC has a dedicated 220 circuit in the panel so I don't know how that could be a factor, however, today when the AC kicks in the other lights dim/flicker.

Are the circuits back on?
Was there a storm recently?
Can you measure the voltage on the circuits that were down?

I suspect an issue with the transformer such that only one half of the box was hot. That is, your house is served by a transformer that supplies you a 'split-phase' circuit. You get +120, -120 and a neutral from the transformer.

There could also be a problem with the AC unit which could either be the cause or a result.

There is a transformer on the pole. All the circuits are back on today. I cannot measure the voltage, although when I checked last night I suspect there was some voltage because the little green 'trip' lights were still lit on the plugs even though the switches didn't turn the lights on. I'm wondering if I should call my electric co to check on their transformer.

Call someone! If you don't even have a way to check voltage you need someone who does!