Will not start

Has the problem actually been diagnosed? By now you've realized throwing random parts at the problem is the least effective and most expensive way to solve it. Other than with diesel engines, you'll never solve a running problem on a Chrysler product by replacing the fuel filter. They commonly last the life of the vehicle unless they rust out and start leaking. If you are able to hear the hum of the fuel pump for one second when you turn on the ignition switch, that will prove it is working. Sometimes that is hard to hear over the chime, then, having a helper listen next to the tank should work. When Chrysler fuel pumps fail, they almost always fail by failing to start up. Once they're running, they rarely quit while you're driving.

The starter relay suggests you're working with two totally different symptoms. If the starter cranks the engine, the starter relay has to be working. On your van, if you crank the engine three times and it doesn't run, the Engine Computer will prevent it from cranking a fourth time until you wait a while. A failure to crank has nothing to do with the fuel pump and filter.

The biggest problem you added was when you replaced the Engine Computer. It is capable of detecting well over 2,000 defects, some of which pertain to crank / no-start problems. It sets diagnostic fault codes that are the starting point in knowing which circuit(s) must be diagnosed. By unplugging the computer or disconnecting a battery cable, the memory was erased and all that valuable diagnostic information was lost.

If you have a crank / no-start problem, two sensors are the common cause of that. The Engine Computer can set diagnostic fault codes for them, but the problem is they often don't set just from cranking the engine. The computer needs more time to detect the missing signals, such as when a stalled engine is coasting to a stop. That means a sensor could be defective even though there is no fault code set related to it.

The first thing we have to know is the exact symptoms and any relevant history that led up to this point. Are we working on a failure of the starter to crank the engine, or does it crank at normal speed, but the engine doesn't run? Once we know that, we can figure out where to start the diagnosis. The complaint "doesn't start" complicates the issue because people use that to describe both of the problems your parts list points to. That's why it's important to differentiate between a "no-crank" problem and a "crank / no-start" problem.

For future reference, the next time a running problem occurs, be sure to read and record the diagnostic fault codes before you disconnect anything. 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 appear in the odometer display. You can go here to see the definitions:

https://www.2carpros.com/trouble_codes/obd2/p0300

or I can interpret them for you. If you missed any codes as they showed up, just turn the ignition switch off, then back to "run" one time, and on most models, the codes will read out again. If you have a crank / no-start condition, it is likely no diagnostic fault codes are going to show since things were disconnected. If that is the case, you'll need a scanner that can display live data. I can describe how to use Chrysler's DRB3 scanner or some of the more popular aftermarket scanners.

Also be aware there is going to be one more common problem caused by disconnecting the battery or the Engine Computer. Idle speed is going to be too low and will cause engine stalling at stop signs, and often a failure of the engine to run unless you hold the accelerator pedal down 1/4". That has a real easy fix, so don't waste any time or money trying to solve that. I'll describe what to do if that becomes necessary.