"SteveH" said:
Could be any of those things. However it could just be that the CPU fan is
u/s. Although it may still be going round, if the speed sensor has stopped
working, your mobo will see the fan as not working and shut the system down
in the manner you describe. So, as they are cheap, try another fan on the
CPU heatsink and see what happens.
SteveH
The BIOS has that fan checking feature in it, on some
motherboards. It might take several seconds for the BIOS
to figure that out, that the fan is too slow.
The Athlon64 and Pentium4 have THERMTRIP, which is an internal
detection of overheat. That signal is connected into the PS_ON#
signal logic that controls the ATX power supply. If the heatsink
falls off your processor, then shutdown in 1 second would be
about right. If the fan is stopped, it might take a bit longer
before the silicon die can heat up the heatsink enough to
trip the overheat detection.
The Athlon(32) didn't have thermal protection built into the
silicon die. But some versions did have a thermal diode, suitable
for monitoring with an external device. Some motherboards, like
the A7N8X series, had a small eight pin chip, that checked the
thermal diode output, and prevented burnout. Some other Athlon
motherboards used their hardware monitor chip to measure
the temperature, but there was no guarantee that the processor
would realize it was overheating in time. And lastly, there
were some other moherboards, that had no protection implemented
at all.
The power supply probably has its own protection logic, and
the complexity of that logic (what it is checking for) depends
on the price of the supply. Overvoltage, undervoltage, overcurrent
are some possibilities, and even internal PSU temps might be
another reason to shutdown.
If the motherboard was faulty, it might just stay off or
stay on. Turning on for a second and then turning off, is
a little too clever for a motherboard on its own

While
I can think of ways it might happen, I've never read of any
such cases.
I would check the condition of the heatsink/fan on the CPU
very carefully. Including, as SteveH has pointed out, that
the fan is still plugged in, and spins when the machine tries
to start. If the fan spins, but the machine still shuts down,
check the heatsink to see whether the clips are still
applying enough pressure to keep the heatsink in contact
with the processor. Sometimes a tab will snap and a clip
will come loose.
And if there is no effective thermal interface material between
the heatsink and the CPU, like you used a thermal paste that
dried out or pumped itself out from between the heatsink
and CPU, that would be another reason for the CPU to overheat.
The material that ships with an AMD or Intel processor, is
not likely to do that, while a hobbyist applied paste is
more likely to leave the scene on you.
Paul