If it were an immobiliser problem you would not be able to bump start the vehicle.
You do not say but hint that intermittently the starter motor fails to turn when you turn the ignition switch to the start position.
This might be a defective switch but I doubt it - more likely a problem down at the starter end of things - you hear no click of the starter motor relay - so I would guess an intermittent lose or dirty connection of the wire that operates the starter relay.
I am not qualified or experienced to offer this advice - others may well offer better suggestions.
Good luck...
December 2014