of course solving the problem means figuring out the cause
(or stumbling upon a fix) one of which hopefully we can do here...
I read back and see you ran Memtest for 12 hours. I think we can eliminate not only the ram but generally consider the motherboard to probably be fine, at least in terms of more major hardware problems. (eg failing components like capacitors).
There are Kernel-Power events as I mentioned, but they merely log that the system didn't shut down cleanly- There are no antecedent and consistent event information before each instance which would suggest a specific cause in each case. This is consistent with a hardware-related problem. Though a system hang as you have described is typically going to point in that direction anyway.
Now, one thing that is sticking out to me now, looking over it again, is a few instances of disk errors like the following
The IO operation at logical block address 0x63d41e3 for Disk 2 (PDO name: \Device\00000047) was retried.
These don't appear consistently before what looks to be the hang issues (unexpected shutdown startups) But it is possible we are only seeing the successful retries, and that there are disk errors which are causing the system to hang when it attempts to retry the block operation- in which case no event data would be written, particularly if the disk affected is the one backing the event log (how do you write data if the drive isn't responding?).
This leads me back to my chkdsk /r suggestion, run in an administrator command prompt followed by a reboot, which performs a full surface scan of the disk. This will take a few hours. It will either find possible bad sectors and mark them bad so they stop being accessed, find no problems and eliminate the HDD as the culprit, or freeze which points at the HDD possibly as having a hardware failure.
There is also the Power Management options If you have any Power management features enabled- processor power saving, etc. in Control Panel, you can try turning those off. incompatibilities or hardware problems can cause attempts to utilize power management capabilities to hang the system.
Beyond that, you could also test the system with a known-good Power Supply (Yes I do see that the PSU was replaced but the replacement could be faulty as well).