Additional info: I have access to air handler in attic but I do not see a C terminal. Connecting the transformer into the C and Rh wire plugs will allow the Nest to be powered separately from the Rc air conditioner wire. My idea to fix the missing C wire issue: buy a 24 volt transformer, and install one wire into the C connector on Nest and the other wire into Rh. Nest seemed to work but in a few hours, the contactor was buzzing and nothing more.
On the old (battery-backed up thermostat), then on the Nest thermostat, red wire went to Rc and yellow wire went to Y. My wiring: a red wire, and a yellow wire.
I think it is Nest taking power from the red wire that is doing it.
