I think if the green neutral light is on then the ecu knows it is in neutral.
If the starter/solenoid clicks then all safety's r met and the ecu is grounding the starter relay
What u need to do is put a volt meter and watch while cranking if it drops below 10 volts then the engine management relay and fuel relay turns off. Sometimes with a click click click and sometimes with just a click.
If u post a video with a volt meter attached i can try to tell u if it is battery or starter solenoid problem
