Our thermostat is 21 years old. It is a Maple Chase. No model number on it. Everything stopped working today. Outside and inside unit. We have replaced the batteries. The thermostat has a display, will change temperatures but the unites are not responding. Circuit breakers have been checked. Two questions
1) - What is the black switch behind the cover?
2) - Any suggestions?

Hot in California!

You might have a bad transformer in the furnace.

Could be a lot of things, contactor, broken wire, bad compressor. With a unit that old, I'd upgrade if nothing else. Switch could be C to F conversion.