5.7 Hemi Swap Tech question

You might get more replies in the new hemi swaps thread.

I don't know if this is any help, but one thing that comes to mind is to check the ASD relay.

Where did you get your harness?
Do they offer any support?
Yes it does sound like the asd relay or the wiring to the ignition switch. If you have it wired wrong it will drop power to the pcm while cranking. I would also look into whether the pcm has skim enabled.