I doubt from your symptoms that is has anything to do with the fuse box like the problem I had.
i am starting to believe it may be the LIM theres little puddles of coolant and oil.
That is definitely not good. You need to remove the SC and lower intake manifold and replace the gaskets asap.
A good scanner should be able to pull all the stored codes to help diagnose the stalling problem.
i just had the same problem as you i had it out the dealership and it took them 2 weeks to figure out it was that causing the startup trouble because it wasn't doing it on every start up but after the fix i haven't had a bad start up yet