No fuel to fuel rail

Don't get stuck on the fuel system. Your description sounds like it's working correctly. The first thing to do is check for spark. Next is to read and record any diagnostic fault codes. Chrysler made doing that yourself much easier than any other manufacturer. Cycle the ignition switch from "off" to "run" three times within five seconds, without cranking the engine, leave it in "run", then watch the code numbers show up in the odometer display. You can go here:

https://www.2carpros.com/trouble_codes/obd2/p0700

To see the definitions, or I can interpret them for you. There's two things to be aware of regarding fault codes. The first is if you're missing fuel pump, (after that initial one second), spark, and injector pulses, the cause is almost always related to the crankshaft position sensor or the camshaft position sensor, and those often do not set diagnostic fault codes simply from cranking the engine. They need more time for the missing signals to be detected, as in when a stalled engine is coasting to a stop. For that reason, don't assume a sensor is okay because there is no code set related to it.

The second concern is fault codes never ever say to replace a part or that one is defective on any brand of car or truck. They only indicate the circuit or system that needs further diagnosis, or the unacceptable operating condition. When a part is referenced in a fault code, it is only the cause of that code about half of the time. First we have to rule out wiring and connector terminal problems, and mechanical problems associated with that part.

Why did you replace the fuel pump? Let me know what you find regarding spark and fault codes.

Go figure. I just got of the phone two minutes ago with a friend who is broke down and he thinks it's his fuel pump. In fact, he has a GMC Suburban and the sudden failure he described is how Chrysler fuel pumps typically fail. What you described is how GM pumps typically fail.

GM fuel pump almost always start up, then they fail while you're driving, leaving you sitting on the side of the road. It is just about unheard of for a Chrysler fuel pump to stop running once they've started up. They fail by failing to start up, leaving you sitting in the driveway or parking lot. The fact you hear it running for one second when you turn on the ignition switch is all the proof we need to know it is running.

The lack of fuel pressure has me confused. If that only happened after you installed the new pump, the likely suspect is you need to put at least five gallons of gas in the tank. There is usually a bowl inside the tank that the pump's pick-up screen sits in. That keeps the screen covered with gas when the level is low and it runs to the side of the tank when you go around a corner. With my '88 Grand Caravan, as soon as gas is poured in, it drops right into that bowl. With my '94 Grand Voyager, it misses the bowl, then it takes a good five gallons before it spills over into the bowl to fill it. At that point, once the engine is running, the fuel coming back on the return line keeps that bowl full so you can run it down to the last gallon.

The flashing Check Engine light was used up to '95 models to read fault codes. After that, they went to standardized three-digit codes, and Chrysler reads them out directly in the odometer display. At some point they stopped including that feature, but I'm not sure which year. I do know I can't read them without a scanner on my 2014 Ram. If you find that, you may need to borrow a simple code reader to see if there's any stored fault codes.

Cutting out intermittently is much more likely to be caused by the camshaft position or crankshaft position sensor. If there is no fault code referring to them, you will need a scanner to view live data. Under the "Sensors" or the "Inputs / Outputs" drop-down menu, the two sensors will be listed with a "No" for each one when the ignition switch is in the "run" position. Those must switch to "Present" or some similar indication, during cranking, to indicate their signals are showing up. If one stays on "No", check its wiring first, but there's about a 50 percent chance the sensor is causing the problem.