Are you saying the fuel pump isn't running during cranking or at any time? It can be hard to hear, but it should still run for one second when you turn on the ignition switch.
The best place to start is by observing the action of the automatic shutdown, (ASD) relay. You can test at any wire that is the same color at every injector, the ignition coil, or even the two smaller terminals on the back of the alternator. A test light works best for this. Digital meters respond too slowly at times. Look for the dark green / orange wires. Back-probe any one of them through the rubber seal alongside the wire. You should see the test light turn on full brightness for one second when you turn on the ignition switch. If you do not, we have to look at the fuse feeding that circuit. I'll search for the diagram if we need it and post that for you.
If the test light does turn on for one second, watch if it turns back on during engine rotation, cranking in this case. If it does not, we have to look at the crankshaft position sensor and the camshaft position sensor in the distributor. Don't rely on the lack of a related diagnostic fault code to determine if they're working. Often the Engine Computer needs more time to detect a missing signal than just from cranking the engine. They usually have to see the signal missing while a stalled engine is coasting to a stop. By far the best way to check these sensors is to use a scanner to view live sensor data during cranking. I have a Chrysler DRB3 for all of my vehicles. It shows each sensor with a "No" or "Present" during cranking. Aftermarket scanners have a similar method of showing that.
If the scanner shows a sensor signal is missing, we can dig into that further. Given the recent history of the transmission, a cracked or broken crankshaft position sensor is the best suspect at this point. They have to be removed before the transmission is removed or replaced.
I posted these diagrams only to show the various places to find the dark green / orange wire. There are seven more diagrams for the engine controls that I can post if you need them. Let me know what you find up to this point, then we'll figure out where to go next.
Images (Click to enlarge)
Monday, May 9th, 2022 AT 8:15 PM