Random Shutdown / Sometimes Reboots - No BSOD Or Memory Dump Files

I have been fighting with my computer for about four weeks now, and I am not getting anywhere. In a nutshell, my computer started to randomly shut down and seldom reboot. There are no specific patterns I notice, except that when I try to find out what's going on the random reboots/shut downs happen more frequently (3-5 time per hour). When I just use the computer, it lasts longer without any issues. I may get between 1-4 hours. No BSOD and no error.

Now when the computer shuts down, it is a hard shut down. It is as if I turned off the power button from the PSU itself and turned it back because when I turn the computer back on, it turns on briefly and shuts down again, turns on again, beeps the all things okay beep, and boots to window. It is worth noting that this behavior started happening without adding any new hardware, software, or driver.

Here's what I have done so far to try to ameliorate/diagnose the issue.

1) I reset the PC - Here's my post on that issue if you want to take a look.
2) I did a clean install - (truly clean install).
3) I boot into the Bios, and it stills reboot/shut down (this causes me to suspect a hardware issue, but what?).
4) I open the case and ensure that everything is properly seated on the MOBO.
5) I cleaned out the PC of dust
6) My temperatures are normal, no overheating going on.
7) I ran ad-ware/spyware check - nothing has been found.
8) I ran a virus check (yes, with windows defender) - nothing came up. I don't think it's a virus since the problem continues even after a clean install.
9) It's not a lack of power issue. My PSU is 1000W and I am not using that much power.
10) I did a stress test for over an hour, and everything was normal (this causes me to doubt it is a hardware problem).
11) I am sure I have done more than the before mentioned steps, but I can't remember them all.

At this point, I suspect my issue might be hardware related; however, I really do not know what this could be, and I do not want to start buying new hardwares (i.e. PSU) without knowing what the issue really is, particularly when it endured a stress test without any issues. I thought of applying a thermal paste/grease on the CPU, but since I am not overheating I don't think that's necessary. So, I am at a lost on what my next steps should be. I am not savvy enough on reading memory dumps files... my computer is not generating any of those files anyway. But I know I can force my computer to generate them.