I am thinking of a sticking relay in the starter circuit. Him locking and unlocking doors sends a few pulses of electric load into the wiring and changes the state of one or another component. Download the FSM and trace from ignition lock to the starter to see what relays and fuses you can attempt to replace.

This was the only approach which helped me to find the root cause of intermittent stalling and not starting years ago, and it was the ECU relay. Nissan is notorious for intermittent electric issues, unfortunately.

 

I'm getting same problem with my 03. Some times fine but sometimes I have to turn key off and then back to start. There will be no start or no crank just nothing even though there is power at the dash. Battery and starter are fine. Ignition switch, who knows. Looking a the starter circuit there is an Inhibitor relay that powers the starter solenoid and also power to the relay coil is through a Park Neutral switch at the transmission. I changed the Inhibitor relay but that's not it. So my next guess is the transmission switch.

Hope you found your problem.
03 Start Circuit

 

It does not happen often, but corrosion of joint connections is also possible. Check them, if you find any corrosion clean and apply a coat of SuperLube dielectric grease.

What's clutch interlock switch? I never had a Nissan with a stick so I dunno.

my 2c.

 

The schematic I've shown is for a manual transmission. Was a mistake, but the auto version is essentially the same. (Park Neutral Start Switch)