I checked this dark green/white wire from terminal M1 all the way to the PCM C1 pin 37 and there is continuity with little to no resistance. I haven’t tested for power at the PCM pin 37 while cranking yet though but seeing that I already did that at M1 I’m assuming it’ll have no power while cranking at pin 37.
So that leads me to think that something isn’t communicating with the PCM seeing that this problem transfers between both of the PCMs I have used for diagnosing.

No offense but you are a mechanically inclined idiot

No offense. But you are.

back up 30 steps then back up 10000 more.

YOU REPLACED A LOT OF COMPONENTS CHASING YOUR PROBLEM. You no longer are facing your original problem and may have very well fixed, created, or indirectly done the other two to previous or future diagnostics paths.

YOU REPLACED THE PCM IN A CAR WITH PASSKEY III+(your key says PK3+?)
FUll stop. STOP. STOP. WHY DID YOU REPLACE YOUR PCM?

WHY?
PUT IT BACK IN, I HOPE YOU DIDNT RETURN IT AS A CORE.

THEN YOU SAID YOU REPLACED YOUR FUSE BOX. WHY DID YOU REPLACE THE BEC ON YOUR CAR? DO YOU HAVE THE ORIGINAL? SHOW US YOUR RIGGING AND HANDIWORK. I DONT SEE ANY PHOTOS! You want help/answers but you have to give us something.
The PCM im pretty sure also grounds the relay, but I guess It may send power, but no offense again but you are smart enough to understand these componentns enough to replace them and how they work, have you ever considered consulting the service data!? They have diagrams and charts that someone like you seems to know how to navigate I assume.

They also have explanation of vehicle anti theft measures and module replacement and reprogramming

Also, "the timing chain itself since I had one and I eliminated the possibility that the timing jumped." beings you replaced it for no reason, I am now telling you that your backfiring has only given reason to believe you did not install the chain properly or you have bad parts. Otherwise, the backfiring is spark plug wiring order or your fuel system rigging is at play or intermixxing with the other possible things. plugged exhaust too for funsies.

please. post pics. back up your "fixes" to their proper working original states, and then also make sure to show us your wiring when you did shotgun surgeon on this car
you dont have to pull the balancer and do those sensors but anythign that can be easily reversed really freaking should be
==============================================

" The original problem with this vehicle started on my way to work when it started to act as if it was trying to stall itself every couple seconds. My first thought was a failing crankshaft position sensor"

Do I need to explain the problem with the highlighted red underlined italics portion is? You never once, NOT ONCE, checked the basics or checked the codes.
If you truly enjoy the guessing and money throwing, thats on you I guess have at it, but please tell me why began that way?

Also I apologize if you have handled anythign I brought up, This website and similar layout have a tendancy to absolutely show a post as being new without replys and then by time you reply you have to scroll the then-present pages of reply to see the recent stuff.

So I did not read replies, if covered, handled, good. but I still stand by the "whys" and "put it back if it wasnt broke"

I've never seen a GM diagram like that one. The PCM applies a ground to energize the relay so your diagram doesn't make sense. Maybe a good scan tool is needed to see if the PCM is receiving a start signal.

No offense taken. The main reason I replaced all those parts is because the car has 214000 miles on it so I figure why not. I’m not ‘throwing parts at it’ I’m just replacing it while I’m there.
Youre right in assuming that I solved the previous problem but now a new one has come up with the PCM not sending power to the fuel pump relay. I replaced the fuse box because the terminals for the fuel pump relay were so loose that it wouldn’t hold the relay in and there wouldn’t be power to the ignition and injectors intermittently. So a new/used fuse box solved that issue.
I 100% guarantee I reinstalled the new timing chain correctly because I got the car running two days ago and the timing is spot on.
Also prior to any of these issues, I replaced the ICM with a brand new one because my girlfriend had an issue with hers so I gave her my old one and I used the new one.

Unfortunately I don’t have an advanced scan tool. I only have one that can read data and scan codes. These diagrams on identifix have been spot on for everything else I’ve tracked down so I think this one is correct. Plus the other inserts for the relay are grounded as they should be.

Can you see if the PCM is getting a start signal? I've not seen any GM vehicle where the PCM applies B+ to the relay. NEVER. I don;t think that diagram has been written right.

Can I check the start signals with a multimeter? And if so do I check it at the PCM?

I’m gonna see if the PCM will ground or send power on my other Buick 3800 to the fuel pump relay so we can either confirm or deny that wiring diagram.

So I figured out that it’* set up exactly the same way on my other car. According to PIN number on the relay, pin 87 has power with key on from the fuse. Pin 30 is the ground side to the fuel pump. Pin 85 is also the ground side to the relay magnet. And finally pin 86 is the power side from the PCM to the relay magnet.
The wiring diagram for that car on identifix also confirms what I found.

This is the wiring diagram for my other 3800 Buick park avenue