The answer to 'why is my ductless system not turning on' is that there could be several common causes, such as a power issue, thermostat problem, or a problem with the indoor or outdoor unit. The system may not be getting power, the thermostat may not be set correctly, or there could be a mechanical or electrical issue with one of the components.
First, check the power supply to the system. Make sure the circuit breaker hasn't tripped and that the power is turned on at the disconnect switch. If the system still doesn't power on, the issue may be with the thermostat. Ensure the thermostat is set to the correct mode and temperature. If the thermostat appears to be functioning properly, the problem may be with the indoor or outdoor unit itself, which would require a professional HVAC technician to diagnose and repair.