Your transmission problem has nothing to do with the no-start condition.
I am a bit surprised that the diagnostic for a no start problem goes directly to the injectors. There are so many thing (cheaper) that can go wrong before first blaming the injectors.
Fuel pump, fuel pump relay, fuel filter, ignition, and about 10 other causes are quite possible.
before spending the kind of money your are talking about, I would have a professional/serious diagnostic done.