OptiPlex 7010 will not soft reset

My refurbished Dell Optiplex 7010 i5-3570 will not successfully restart from a soft reset from the installed operating system (pfSense v. 2.4.4) or from a bootable USB with firmware updates. After selecting "reboot" from the system menu, the system appears to perform the OS shutdown, but the processor fan spins continuously, the USB key light shuts off (but never turns back on), the power switch LED stays on solid, and the system never shows the DELL logo splash. This happens with BIOS versions A20, A25, A26, A28, and A29. I have tried with and without USB drive / mouse / keyboard attached, with my monitor attached to onboard VGA and D-Port (with a D-Port to VGA adapter). The USB drive is important in the diagnosis only because I can tell whether or not the system is going to restart based on whether or not the USB key lights up or not. All USB devices are attached to the front USB ports.

When the failure occurs I have to force power off by holding down the power button until the LED shuts off, then use the power button again to re-start the system at which point it will boot normally.

This failure occurs (as mentioned above) even when I try to update (or downgrade) the BIOS from a bootable USB. The upgrade (downgrade) starts successfully, but the system will not reboot successfully to complete the operation. The only way I have been able to transition between BIOS versions is by using the CMOS reset to force the BIOS into an error condition (time / date not correct) in order to boot to USB and flash the BIOS, but I am not convinced that even this would work after several minutes, as the failing state sometimes will not show up until an hour after the last successful reboot.

My system configuration is as follows:

Stock OptiPlex 7010

Intel 4 port GB ethernet PCI-E adapter (EXPI9404PTLBLK) in the lower PCI-E slot (x4)

8GB DDR3 RAM as 2 Hynix HMT451U6BFR8C-PB 4GB sticks at 1600 MT/s in slots 1 and 2

SanDisk SSD 248GB hard drive

I have no GPU installed and am using the on-board video.

I have tried the following BIOS settings:

Legacy BIOS

UEFI bios with and without Legacy ROM support

With PCI device support turned on and off

With all S3 / C-State settings turned on and off

With keyboard error reporting turned on and off

All AC power restore settings (On / Off / Last State)

I have also replaced the CMOS battery and unseated / reseated all devices.

I really need to be able to complete OS updates and other functions remotely, so I need some help figuring out why this system will not restart successfully. Any thoughts will be appreciated. I've scoured the web for others with this issue, and the closest I have come is someone saying that they have abandoned Windows updates because of a similar issue.