The answer to 'my thermostat won't turn on' is that there are several common causes, including a dead battery, a wiring issue, or a faulty thermostat. The first step is to check the batteries and replace them if needed. If that doesn't resolve the issue, you may have a problem with the wiring connections or the thermostat itself.
If the batteries are good and the wiring seems intact, the thermostat may need to be replaced. This is a relatively simple DIY repair for most homeowners, but if you're not comfortable working with electrical components, it's best to call a professional HVAC technician to diagnose and fix the problem.