Thanks for requesting me!
With this set, unless both the stator and rotor happen to be shot, definitely fix it. It's too bad you have already replaced an expensive controller.
Code 36 is almost always fuel related.
As far as the shutting off when you release the start button, this is the single most common complaint with Onan. It has several causes, but is most often caused by the set not producing electricity.
The first thing you need to do is to verify whether the set is actually producing or not.
Remove the control cover to access the circuit breakers. Set your meter to VAC and connect the negative lead to a good ground. Connect the positive lead to the back of a circuit breaker on the wire marked T1. Press and hold start for about 5 seconds.
How much voltage is being produced?
I am also assuming you have checked the oil level to ensure it is full.