fuel pump, coils and injectors all get their power from the same pin of the start relay. the ECU shuts that system off after 2 seconds to prevent the fuel pump from running constantly if the engine is not running. And turns it back on with engine crank. I don't see anything on the engine side of the system that would prevent the engine from cranking. So I would be concentrating on what is preventing power to the starter solenoid in the crank position. Something is not working properly between the key switch in the start position and the starter solenoid on the engine. Did you also check the PTO switch. Whatever is preventing cranking is likely also effecting pin 3.
What happens if you ground pin 3 and then jump the solenoid to crank the engine. Pin three may be ground to run.