How similar a load? Things like a couple more hard drives
and the gaming video card can be significant enough
difference in load to have an effect.
Since there is this variability, it seems unlikely it would
be something overheating... if the heatsink weren't on good
enough to even allow it to finish posting, it wouldn't
magically make a good enough contact other times to boot
windows, unless you had a very strange environment where the
ambient temp plunged very low on occasions where it'd boot
windows.
If you have a hardware monitoring software installed, check
it for shutdown settings/thresholds. That's certainly not
what's shutting it down before windows even loads, but as
with bios, software could cause this given the same problem
whatever it may be.
Try leaving the system sitting in the bios hardware
monitoring/health menu, watching temps/voltages/fan-RPMs,
and see if it will just sit there at the bios menu
indefinitely or if it still shuts down, and if/when it shuts
down if any of the things you're watching have significantly
changed.
You didn't mention what make, model, and ratings for 12V
power your PSU has. Offhand I would still suspect the PSU
is insufficient. What exactly do you have to do to get the
system running again when it shuts down (I assume shut down
means completely off, no fans or anything running,
correct?)? Can you press the case front switch or must you
flip the PSU rear switch (If so equipped) or unplug it from
AC?
All fans may be running but if any are running slower than
(very roughly) 1000 RPM then the motherboard may have
trouble detecting them. If this were the case then you
could temporarily unplug any fans in question to see if the
system immediately shut down. Nothing will overheat enough
to matter by having the fan unplugged for such a short
period, you can just power off the system to more safely
take your time to plug the fan back in.
It's not windows, not files or any kind of added data
problem, that would not have any effect on a system that was
turned off, then powered on, since it hasn't loaded any of
that data from the hard drive yet when it boots - since it
sometimes shuts down before then.
One way to check whether the PSU is overtaxed would be to
temporarily put a less power hungry video card in, and
reduce number of hard drives and other things not critical
to running windows for a short test whether the shutdown
problem is lessened. You didn't tell us the frequency at
which it occurs. Once a month? Every 2 minutes?
Inspect the motherboard for failed capacitors, and if
nothing else seems to help, leave PSU unplugged from AC for
a few minutes then open and inspect it as well (unless doing
so would void a warranty still in effect).