The answer to 'ductless system not turning on' is that there could be several common causes, such as a power supply issue, a problem with the thermostat or remote control, or a mechanical failure in the indoor or outdoor unit. Symptoms may include the system not responding to the thermostat, the display not turning on, or the unit not running at all.
Some potential solutions include checking the power supply, inspecting the thermostat and remote control for any issues, and verifying that the indoor and outdoor units are communicating properly. If you're unable to resolve the issue, it's best to call a professional HVAC technician who can diagnose and repair the problem.