Dear community,

I have a Dell T620 that shuts down randomly. I could be in the BIOS /Lifecycle Controller/Proxmox screen and the shutdown could occur. No power to the front, no power to IDRAC. Running a full hardware diagnosis shows no hardware issues. I need to coax the server to boot by unplugging both PSUs for, usually, an hour, then plugging it back in. When I can power on the server, it could run for 10 minutes or a week. Lately, I *feel like* the times the server is running are getting shorter. 
The lifecycle log does not note anything except when I finally coax the server into booting again, the following entries are always displayed with the timestamp being the minute I can get the server powered on and not when the server went down. 

(Pulling from memory as I can't get to the logs at this exact moment) 
4th event -Something about CPU reseating-
3rd event The iDRAC firmware was rebooted with the following reason: ac.
2nd event Power Supply 1: Status = 0x00, IOUT = 0x0, VOUT= 0x0, TEMP= 0x0, FAN = 0x0, INPUT= 0x0
1st event Power Supply 2: Status = 0x00, IOUT = 0x0, VOUT= 0x0, TEMP= 0x0, FAN = 0x0, INPUT= 0x0

Both PSUs are Delta 750W PSU (PN: 5NF18) on the latest possible firmware: 07.2B.80
PSU1 is connected to a UPS (UPS is not wired to the Server, so no shutdown signal and no logs on the UPS that point to anything strange). PSU2 in a traditional outlet. Both PSUs have a solid green light. The peak power draw is roughly 300W.

With the server working intermittently, I may have fallen for some possible red herrings (not in any particular order):
Replaced the power distribution unit 
Tried re-upgrading the PSU firmware 
IDRAC reset 
Using expletives 
Swapping PS1 and PS2
Using one PSU in slot 1
Using one PSU in slot 2
Taking apart the server and visually inspecting all boards for any sign of blown caps or burns/shorts. 

Things I haven't tried yet: 
Bought new (technically used/refurbished) PSUs 
Motherboard replacement

IDRAC7 - there are no logs that mention anything about "watchdog". IDRAC is integrated into this board. 

Anything else I should be looking at troubleshooting? 

Best, 
Randy