Where is the fuel pressure regulator located

If the starter will not crank the engine, why are you working in the fuel supply system? Do you hear a single, rather loud clunk from the starter each time you turn the ignition switch to "crank"?

The fuel pressure regulator is on the fuel rail on the engine. It has an uncommonly low failure rate. I have only read about two leaking since the early 1990's. Both of those were on throttle body injection systems.

So there is nothing wrong with the starter. I suspect what you are seeing from the tail pipe is condensed water vapor that was sitting in the muffler.

It sounds like fuel pressure is bleeding off when the engine is stopped. It has to build up high enough before fuel will spray from the injectors. The fuel pump will run for one second when you turn on the ignition switch. That is supposed to be enough in case pressure dropped a little, but if it dropped all the way to 0 psi, it will take longer than that, especially since the battery voltage will be lower during cranking.

There are two things you can do to verify if pressure is dropping too much. The best way is to connect a fuel pressure gauge, then watch what happens to pressure over a few hours. It should not drop very much over many days to a couple of weeks. As an alternative, turn the ignition switch to "run", wait for the fuel pump to turn off after about one second, turn the ignition switch off, then to "run" again. Do that a third time, then crank the engine. If it starts right away, suspect fuel pressure was dropping.

Four things can cause the fuel pressure to drop. By far the most common cause is a leaking injector. You will need to remove the fuel rail with the injectors, flip it over so you can see them, then watch for any that become wet after the system is pressurized. Pressure can take hours to bleed off through a leaking injector, and it may stop dropping once it has reached a certain pressure.

The check valve in the fuel pump can leak, and the fuel pressure regulator can leak. Both of those are very uncommon. To identify a leaking regulator, use a hose pinch-off pliers to pinch the fuel return line where it is a rubber hose between the fuel rail and body. To identify a leaking check valve in the pump, pinch the larger fuel supply line the same way. Also pull the vacuum hose off the regulator and check inside it for wetness. If you see gas in the hose, replace the regulator. That is a real common problem on GM trucks, but not on Chrysler products.

The fourth thing to consider is the o-ring on the fuel pressure regulator. I ran into two of those that were cut; one on a brand new car just delivered to the dealership. Fuel pressure will bleed off almost instantly when the engine is stopped. Crank time will be real long to get the engine started, and unlike with a leaking injector, cycling the ignition switch repeatedly before cranking the engine will not help. Fuel pressure will bleed down to 0 psi before you can get the switch back to the "run" position. The only way to get pressure high enough for the engine to run when the o-ring is leaking is for the fuel pump to run non-stop, and that will only occur during engine cranking.