Any hard to start to diagnostic usually begins by checking for spark, fuel pressure, injection pulse, and the essential PCM inputs such as the camshaft and crankshaft sensor signals, ambient air temperature, engine coolant temperature, along with the MAP (manifold absolute pressure) and TPS (throttle position).
When someone says they have to use the throttle to help start the car there are a few things that do come to mind and one of those is that the engine is getting too much fuel and is flooding. If the idle air control valve isn't opening correctly that could allow insufficient air for the fuel that is being delivered essentially creating the same result. Does this blow black smoke and labor up to speed when it does start? Weak spark could do the same if the fuel system is delivering fuel but the coil pack unable to fire the plugs.
Some other things I would want to know if you were going to drop this off for testing is once it starts, how long does it need to be turned off to present the symptom again? A few hours? All day? Overnight?
Are any other short term shut downs and restarts problematic? Does ambient temperature or humidity play a role?
temperature has not played a roll- problems with restart generally take a few hrs hot engine starts fine short term shut downs after driving for several miles lets say 15 motor has stalled out at stop lights if you do not brake and throttle at same time this is not always the case more of an occasional issue and yes if motor does start without help of accelerator it labors greatly and while black smoke is not present the smell of load up (flooding) is very evident-then motor will idle around 400 rpm for a minute or so until it cleans itself up then idle is between 900 and 1000 rpm i am not a "skilled" mechanic i am able to replace parts I did consider the coil pack also however before i continue with the might fix its just looking for more detailed ideas