The answer to 'my HVAC system won't turn on' is that there could be several common causes, such as a tripped circuit breaker, a faulty thermostat, or issues with the HVAC unit itself. The first thing to check is the circuit breaker - if it has been tripped, simply reset it and see if the system powers on. If the breaker keeps tripping, there may be an electrical problem that requires a professional HVAC technician to diagnose and repair.
Another common issue is a malfunctioning thermostat. Make sure the thermostat is set to 'cool' and that the temperature is set lower than the current room temperature. If the thermostat appears to be working but the HVAC system still won't turn on, the thermostat may need to be replaced. For this and other more complex issues, it's best to call in a professional HVAC technician to properly inspect and repair the system.