A couple of things come to mind reading through this thread. The first is that if you hold your hand over the throttle body it will start each time. This says to me that perhaps the IAC is not in the correct position allowing too much air into the engine while you crank, when you choke off the air it starts. Also the fact that it runs fine when it does run would indicate that the IAC IS working which would mean you probably have a control unit issue. Since the computer has been replaced twice and the wiring apparently has been verified there is one more clue to this that has me thinking. I’m a little confused at how the engine will crank and suddenly stop. If you put this together with what’s happening when you put your hand over the throttle body and it does start I’m left wondering if you have an ignition switch problem. If the ignition switch doesn’t send a signal to the computer to set the IAC the IAC will not set. Also if the ignition switch does not send a signal to the starter or that signal is interrupted then the starter will stop cranking midway. If it were me I’d be verifying the operation of the ignition switch to see if it’s sending out the signals it should.
Keep us posted.