A bad thermostat and a bad air conditioner look identical from the hallway: the house won't reach temperature. Telling them apart before you call saves you from paying to diagnose a $200 problem as a $2,000 one.
A blank or dead screen is the obvious one, and it's often just batteries. Many thermostats that look wired still use batteries for the display, and a dying set produces erratic behaviour long before the screen goes fully dark.
Set temperature and room temperature disagreeing noticeably is another. If the thermostat says 78 and a separate thermometer on the same wall says 72, the thermostat is reading wrong and the system is responding correctly to bad information.
A system that won't turn on at all, or won't turn off, also points here — especially if it responds to nothing you do at the thermostat.
Set the thermostat well below the current room temperature — drop it ten degrees — and listen. If the outdoor unit kicks on, the thermostat is successfully calling for cooling, and your problem is downstream in the system.
If nothing happens at all, and you've confirmed the breakers are on, the thermostat or its wiring is a strong suspect. That's a useful thing to be able to tell us on the phone.
Do the same thing with heat: set it well above room temperature and see whether the furnace fires. A thermostat that calls for one and not the other narrows things down considerably.
A thermostat in direct sunlight reads warmer than the house and runs the system too long. One above a lamp or near a kitchen does the same. One on an exterior wall, or with a duct running behind it, reads a temperature nobody in the house is experiencing.
None of those are broken thermostats, but they all produce the complaint "the house never feels like what the thermostat says." Moving it is a real fix, and it's worth identifying before anyone buys a replacement.
A smart thermostat installed without a C-wire has to steal power from the control circuit to stay alive. That can make a system short cycle, or make the thermostat drop offline repeatedly. If your trouble started right after a new thermostat went in, that's the first place to look.
Heat pumps are pickier still — they need a thermostat that controls the reversing valve and auxiliary heat correctly, and the wrong one can run expensive backup heat when it shouldn't. Compatibility is worth confirming before buying, not after.
We diagnose the whole system, so you won't pay to replace a thermostat that was never the problem.