The central air unit outside will not turn on but at the thermostat it says its on? Tried circuit breaker, batteries, disconnecting thermostat from wall etc

We changed batteries in our thermostat when the blinking battery icon came on but the icon never stopped blinking and we don't have any heat. The fan comes on but nothing else. We purchased an new thermostat (same model) and no change. Same blinking light. What does this mean? Is it a thermostat...

I'm replacing a 23 year old manual Honeywell thermostat with a new digital Honeywell thermostat model RTH111. The old thermostat has two wires (colors white and red) but no designation on the terminals. This is for a hot water baseboard gas fired boiler. Which terminals do these unmarked wires...

I replaced the batteries in my Honeywell RTH110B thermostat with the air conditioning running contrary to the instructions that I read afterward. I am now getting a blinking snowflake air conditioning symbol but no air. How can I fix this problem? Thanks