The answer to 'my replacement won't turn on' is that there could be several common causes, such as a tripped circuit breaker, faulty wiring, or a problem with the thermostat or control board. First, check the circuit breaker and reset it if it has tripped. If that doesn't work, inspect the wiring for any loose connections or damage. You may also want to check the thermostat settings and replace the batteries if it's battery-powered.
If the issue persists, it's likely a more complex problem that will require a professional HVAC technician to diagnose and repair. Attempting to fix the issue yourself could be dangerous and may even void the warranty on your new HVAC unit. It's best to call a licensed and experienced HVAC contractor to properly troubleshoot and repair the problem.