New system build - reboot loop when attempting to boot from SATA HDD

This is a new system build that fails to boot from the SATA HDD.
Instead, it appears to power down and restart, in a loop.

Mobo: ASRock Z390 Taichi (original BIOS P1.20, since updated to P1.80)
*RAM: G.Skill Ripjaws F4-3200C16Q-64GVK (4x16GB)
*CPU: Intel Core i7-8700
Asus optical drive scavenged from parts drawer
Samsung 2TB 5400RPM SATA HDD scavenged from parts drawer
PS2 keyboard
USB mouse
Onboard video (also tested with older PCIe video card)

*The CPU and RAM are on ASRock's approved compatible list for this mobo.

With all parts on hand, I built the new system on a non-conductive
table, using the mobo's non-static envelope for additional protection. I
like to do the initial build outside of a case to make sure everything
works before I go to the trouble of physically installing everything
inside the case.

The CPU and stock cooler installed without issue, with the stock cooler
coming from the factory with heat transfer compound already applied. I
installed a single memory module in slot A1 (closest to CPU). I
connected a known working PSU (Corsair vx550w), the PS2 keyboard and the
USB mouse. I connected a monitor via HDMI to the onboard video and fired
it up. No optical drive or HDD connected at this point. The PSU is
connected by the standard 24-pin connector and the 8-pin EPS12v
connector. The mobo has a separate 4-pin ATX12v connector, which remains
unconnected. ASRock tech support says that's fine.

With no boot devices connected, the system came up directly in the BIOS
screen, where everything looked normal. The CPU and RAM were recognized;
the CPU fan RPM was reported as about 1580 RPM and CPU temp at 34C
(later stabilizing at about 38-45C, depending on activity).

I shut it down, plugged in a USB thumb drive with Memtest+ 6.00 on it,
and started back up. As the only available boot device, the system
automatically booted into the Memtest program. (Fast forward here, but I
tested an individual RAM stick in slot A1, then B1, then A2, and finally
B2. Then I jumped ahead and installed all 4 memory modules and let
Memtest run overnight. Absolutely no issues so far, but I removed all
but the A1 module before proceeding to the next test.)

Next, I removed the Memtest USB thumb drive and connected the optical
drive via SATA. I inserted a known good Linux Mint 19 disc and started
the system. The 'live' Linux environment came up without any issues. I
temporarily connected the breadboard system to my LAN and browsed the
net for a period of time to watch for issues, but everything was fine.

Next, I shut down and connected a single Samsung 2TB 5400 SATA HDD and
restarted the system. Again, I booted the Linux live environment, but
this time I elected to install Linux to the HDD. That completed without
issue. The next step would be to boot into that new Linux install.

When I was ready, I removed the Linux disc from the optical drive and
rebooted, expecting the system to boot into Linux from the HDD. I got to
the expected grub menu, where I have 4 choices and the first choice is
the default: Linux Mint 19. Pressing Enter or allowing the timer to
expire, the next thing that happens is all of the LEDs (there are quite
a few on this mobo) go out, the CPU fan stops spinning, and after 2-3
seconds, the system powers up again, repeating the behavior described.
It gets to the grub menu, then whether I intervene or not, it powers
down and restarts, in a loop.

===
Status so far:
Stable in the BIOS screens with no storage devices connected.
Stable in Memtest when run from USB thumb drive.
Stable in the live Linux environment when run from optical disc.
**Unable to boot into Linux from the SATA HDD.**
===

I grabbed a second Samsung 2TB SATA HDD and different SATA cable, then
installed Linux to that drive. I got exactly the same behavior described
above.

Next, with the SATA HDD still connected, I chose the Memtest option from
the grub menu. A slightly older version comes up, 5.01 rather than the
6.00 that I have on the USB thumb drive, but Memtest comes up and runs
successfully.

Thinking it's possibly a too-weak PSU at 550W, I swapped in the 650W PSU
from another working system, a Corsair tx650w, but it made absolutely no
difference, so I went back to the 550W unit. Online PSU calculators tell
me that I need between 230W and 340W, depending on the calculator, so
adding a bit for headroom they think I should be OK with 350W to 450W,
indicating to me that 550 and 650 are well into the safe area.

Thinking it's an overheated CPU, I can see in the BIOS screen and in
Memtest that the CPU temp hovers at 38-45C, but usually stays right
around 40-41C. The heat fins on the CPU cooler appear to be at room
temperature, but then I'm only running Memtest or viewing the BIOS
screens, so not any appreciable load. (Yes, it's UEFI, but I'm used to
calling it BIOS.)

Thinking it's RAM that's not being properly recognized, I see in the
BIOS that it's recognized as exactly what G.Skill says it should be:
"DDR4-3200 PC4-25600 CL 16-18-18-38 1.35v"

ASRock suggested RMA'ing the mobo and Newegg agreed, so I did. When the
replacement arrived the other day, I repeated all of the steps listed
above and eventually arrived at exactly the same place:

===
Status so far:
Stable in the BIOS screens with no storage devices connected.
Stable in Memtest when run from USB thumb drive.
Stable in the live Linux environment when run from optical disc.
**Unable to boot into Linux from the SATA HDD.**
===

Beginning to doubt the integrity of the Linux DVD, even after its
integrity check was successful and it's a disc that I've used
successfully before, I downloaded and burned the latest Windows 10 ISO.
Booting from the Windows 10 disc, I get to the point where it starts to
copy files to the HDD, then the system powers down, LEDs and CPU fan
off, then 2-3 seconds later it powers up again and starts the Windows
install from scratch. Even though I was able to install Linux twice on
the first HDD and once on the second HDD, I couldn't get the system to
stay up long enough to get Windows installed. I also tried burning the
Windows 10 ISO to a USB thumb drive, but I couldn't get the system to
stay up long enough to get Windows installed that way, either. BTW,
there are 8 SATA ports on the mobo, 6 on one controller and 2 on another
controller. I tried SATA ports from both groups.

I'm currently on page 58 of 491 pages on the ASRock forums, and so far
I've seen two others with a "system powers down and restarts" issue, but
no resolution provided.

I've built at least several hundred PC systems for people since the
early 1990's, most of which have gone smoothly, but this one currently
has me stumped. This build is supposed to be for me, if I can get it
working.

At this point, I'm not sure where to go next.
- Is it running out of power? Do I need a newer, bigger, PSU?
- Is there an issue with the CPU?
- Should I chalk this expensive mobo, my first ASRock, up to experience
and go with something from ASUS or Gigabyte?