I connected an HDMI monitor to my F4-223 and fiddled with the BIOS settings. I do not have exact recollection of what settings I changed, but having over 20 years of experience with computers, I highly doubt that I would have changed anything critical and not something benign like boot order. Nevertheless, after turning the unit off and back on, it now: 1) doesn't show anything on the screen, 2) sits for like 3 seconds, and then 3) clicks its speaker and shuts off.
"OK, maybe I DID mess something up!" I thought, removed the CMOS backup battery and waited for a full day before reinstalling the battery and turning it on again -- that time should be enough for the CMOS to lose charge and BIOS settings to reset to default. Surprisingly, that did not help! The behavior did not change.
Also there's a button in the motherboard that I assumed may be CMOS reset -- but turning the box on with that button held doesn't solve the problem either.
Now I am out of ideas.

I have never heard of "bricking the box by changing BIOS settings".
Any suggestions?