I've searched alot, on here, and google, but haven't found the definitive answer.

2001 CL, flat out quit running while driving, as if the key got turned off. It's been randomly doing this for the last week or so, but always starts right back up just fine. This time tho, nothing. Turn the key to start it, not even a click. Dash lights do dim a slight bit, but motor doesn't turn over at all. I jumped the cables at starter, it'll turn over just fine that way

I know the PGMI is problematic anyway, gonna replace it anyway, but would it cause the engine to not turn over at all? Or just cause it to turn over, but not to actually start?

 

I had an issue with my fuel pump where I was at a red light, and she just turned off in the middle of the street. Thankfully, some people helped me push it to a gas station where I had it towed later that night.
Had it replaced with a brand new fuel pump, happened again. It took me replacing it with a junkyard fuel pump in a FedEx parking lot for the issue to officially go away. I also resoldered all the connections on the PGMI relay just to be safe, as well as swapping it out for another.
My girlfriend also had the same issue with her car not starting, but would crank. I fixed that by also resoldering the joint on her PGMI Relay.

So I guess the fix for your issue is either a new fuel pump, or resoldering the joints in the PGMI relay.

 

So I was thinking about this last night, and I was reminded that I actually replaced the entire assembly. Whenever my car would crank, but not start, I'd give the plugs to the fuel pump assembly a light smack until she's go.
So along with the fuel pump, check the assembly.