Get it away from that dealership. A parasitic draw would mean something in the vehicle would drain the battery while it sits. A boost or battery charge would start the vehicle if that was the problem. Putting it in neutral and rolling it wouldn't correct a draw. They're going down the wrong avenue.
Take me back. Have you tried just starting the engine with the shifter in neutral before this. Or was this your first shot at "neutral, roll it, put it in park and then start it" text me if you like at 613-847-fife-nine-ate-fife. Especially during a no Start attempt. We will find and fix this problem.
---------- Post added at 07:22 AM ---------- Previous post was at 07:19 AM ----------
Also does it have a remote starter (factory or aftermarket) Does it normally work properly, and if so have you ever stood back from the vehicle during a no start event and tried the remote starter?