After completing a motor swap, the engine cranks but does not start

Hello, do you know if you are getting Ignition Spark? or any pulse from the Fuel Injectors? If you have everything hooked up correctly, not missing any Ground connections or anything like that, there might be a difference in the Crankshaft position sensors signal. If they changed the reluctor wheel design between 1995 and 98 and for example in 95 the crankshaft reluctor wheel had 53 teeth and they changed it to a different size or number of teeth. This car has a camshaft position sensors as well, so if the crank and cam sensors are not in sync, you'll be lacking spark or injection pulse. Here's a couple guides below, I'll look up the wiring diagrams and see if there are any notable differences. But see if you are getting any spark, if you are try getting it to start with some alternative fuel source. I quick spray of starting fluid will tell you if you're missing a fuel supply. Just don't spray the Mass Air Flow sensor on the air intake boot, spray it in through the brake booster hose or somewhere else.

Okay, I did find some differences here. On the 95 the Crankshaft Position sensor sends a signal to the Ignition Control Module (ICM) first, and then the signal is sent to the PCM. The PCM then outputs a square wave signal back to the ICM. So, the crankshaft position signals might be the same (variable A/C voltage signal) but there is probably a difference in how the signals are processed. The 98 crankshaft position sensor reluctor ring has 36 teeth on it, there's no number of teeth for the 95 listed, but if you still have the motor, you could check it.
The crank sensor on the 98 goes directly into the PCM, whereas the 95 crank sensor signal goes to the ICM first, then to the PCM and then back to the ICM. If there is a SPOUT connector near the distributor you could try unplugging, it. That would set the spark timing to base timing and there would be no signal processing happening. It might start then, but you couldn't leave it like that because it would always run at only 10degrees base timing and you might have some engine knock occurring., My guess is that the crankshaft reluctor wheel has a different number of teeth though. It looks like they made some pretty big changes between those years. But take a look at the old engine if you can and see how many teeth are on the crankshaft. Maybe there is a way around whatever is causing the no start.

Okay, the last picture is supposed to be from 1994 to 1998 3.8liter and it has 36 minus 1 tooth so that's correct. So technically speaking it should work. So, I would check for spark, see if you're missing that or fuel injector pulse (which you can check with a test light) in the guide below. So, start there, maybe there is just a bad connector somewhere that has a pin fitment issue.

https://www.2carpros.com/articles/how-a-crank-shaft-angle-sensor-works

https://www.2carpros.com/articles/how-to-test-a-fuel-injector

https://www.2carpros.com/articles/how-to-check-for-ignition-spark

Oh, okay, you did get it running. Thats good, I'll look up the transmission spec for you. It uses Mercon(R) Automatic transmission fluid. Refill capacity is 13.9q. I would measure what's on the stick, fill it up to level, then run it until its warm, shift through all the gears, this gets fluid into all the necessary ports, allow it to get to full operating temperature, shift it through all the gears again just to be sure, then add as needed.
I honestly have found that when replacing the transmission fluid on a regular basis causes a transmission to wear out faster. Thats what I've seen. So, I would just fill what you need but run it through the process, so you know you're getting it completely filled. The specs are below. Hope it goes well for you.