I assume it is the 3.0 petrol not diesel. I can't see how pushing the car back in neutral can make any change to the starting sequence of an engine.
When you say it won't start do you mean that it turns and turns but doesn't fire but then intermittently it will start no problem?
If it is diesel it is a totally different ball game but if its petrol you need to check your live data, trims, and see if any pending codes are there, not stored codes. It literally could be many things, it may be worth removing and cleaning cam and crank sensors as after 120k they will be very dirty if never replaced from new and will not tell the ecu that you are turning the engine over and trying to start it.