I don't want to speak too soon but I believe I can marked this thread solved. After installing the two new sticks of memory in both the blue slots of the mother board and having the BIOS at stock, I have not encountered any BSOD. I ran memtest for 15 passes and it had 1 error but i think it was a false error. I also ran prime95 blend test for 6+ hours with no errors. I've been able to shut down the computer over night and turn it back on with no issues. I've also been able to quickly resume from hibernation where before it wouldn't work.
I appreciate everyone's help in getting this issue solved and I've learned a lot from this experience.
@DeanP Should I still update that driver
if I'm not having any issues?