Sounds like the Sentry system bugged out to me. I've never seen injectors start then stall. They can develop excessive spillback and cause a long crank time, or crank no start. They skip, smoke, misfire, knock, burn holes in the pistons but I've not seen one cause a start then stall.
The test they want to run is a spillback test, but it doesn't sound appropriate to your concern. If the no start was fuel related, it can be found by a simple data check while cranking, the fuel system will never achieve the 4,500 psi necessary to start. Then you do spillback to find the faulty injectors.
I think a $450 Sentry module might be in your future. As well as some new keys and a lock cylinder.
The fuel lift system on that is electric in tank pump, I do put a lot of pumps in them, though. If the lift pump is weak, it can trap air in the system that it cannot drive back down the return lines.