Have you tried depressing the clutch when you press the start button?
With my auto RX there are a couple of different options similar to the first turn of the key - ignition on so radio can play etc but no starter circuit engaged. It was possible to get it stuck in a cycle that stopped you starting the car. The way to break the cycle was to press the start button without hitting the pedal so all the lights went off. Close all doors, activate alarm, deactivate alarm and press start button with brake pedal engaged (to start auto)
You may have a similar switch which allows the car to differentiate between limited internal 12v live and full starter cct activation