Intermittent issue of the vehicle not accelerating?

Even though you have no check engine light on there still can be a code, also does the exhaust sound okay. I have seen catalytic converters come apart internally and intermittently block the exhaust outlet causing the problem you are describing.

Here are two guides that can help:

https://www.2carpros.com/articles/engine-has-low-power-output

and

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

You could have a fuel pump that is going out as well, if the exhaust is okay with no codes let's do a fuel pump pressure test.

Standard fuel pressure 304 to 343 kPa (3.1 to 3.5 kgf/cm2, 44 to 50 psi)

This guide can help and you can rent a fuel pressure test gauge at the auto parts store free cheap or free in most cases:

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

Please go over these guides and report back.

Yes, I have taken the catalyst apart and checked. I also have run a fuel pressure test on it, even while driving.

I have a feeling it may need a PCM.

It sounds like it could be, but to be sure we should run a CAN scan, you can get a CAN scanner (Controller Area Network) from Amazon from about $32.00.

Here is a video to show you how:

https://youtu.be/u-4syLc-ifQ

and

https://www.2carpros.com/articles/can-scan-controller-area-network-easy

Here is the PCM location and how to replace it. Check out the images (below). Please let us know what happens. You can get a rebuilt PCM by searching google or eBay. That way it will be preprogrammed.