Strange boot up issue - need help please?

Hi guys!

I hope some of you might have an idea on the following issue. Any idea will
be greatly appreciated!
I just assembled 4 identical pc's (the first time I assemble my own pc).
I made sure, that every connector is assembled the same way.
But the pc's react differently when the power cable is connected to the PSU.
Let me specify what I experience:

1. I connect all relevant peripherals (mouse, keyboard, monitor etc.)
2. I plug in the power cord to the PSU.
3. When I switch on the power switch on the back of the case the pc's do the
following:
2 of the pc's stay off, and you have to press the ON button on the front
of the case to boot up the pc's (this is the way I expected it to work).
1 of the pc's turns on and boots up immediatly.
1 of the pc's turns on the power (fans start, harddisk led turns on),
but the "power led" stays off, and the pc doesn't boot up. Then if you press
the ON button on the front of the case the pc boots up.

This strange behaviour is only seen, when the power cord has been plugged
out and in again.
Does anyone have an idea, what might be wrong here, or why the 4 pc's (which
have identical components) react in these 3 different ways???
I have tried to search newsgroups, but couldn't find anyone with the same
problem.
The motherboards are "MSI K8N Neo2 Platinum 54g" and the case is an Antec
Sonata with integrated Antec 380W PSU.

Thank you for any help at all!