A bad fuel pump relay or dead fuel pump circuit in the ecm will act like this. I just went through the same exact thing on a GN. Ended up the the fp circuit in the ecm was dead. Contrary to what most people think The oil sender bypasses the fuel pump relay and toggles the fuel pump but when the car is warm the oil is thinner and the switch in the sender does not always close when cranking a hot motor. Very weird. DR BOOST explained to me how it worked. It took a while to grasp the concept but made sense once figured it out.
Just maybe this might be your problem.
First, unplug the the oil sending unit. It's behind the lower radiator hose on the engine. Just pull the plug off then see if the car starts. Post back with results.
