P4B does not boot after power ON but boots on soft power ON

A computer running P4B is not able to boot when the power supply is
switched OFF and then ON. Switching ON the power button of the power ATX
supply just makes the mobo green LED flicker, the activity yellow LED
flicker and the green front power LED ON. The fan of the CPU spins. But
the BIOS never gets started. I am not sure how it happens, but after a
while of fiddling with the power button(in the front) and the reset
button the flickerning LEDS gradually decrease their flicker frequency
and then the mobo powers off. Only after this can i use the power button
in the front to power ON the computer and BIOS works just fine. From
this point onwards, as long as I do not shut off the main power, I can
switch ON and OFF the computer from it's front power button properly.

What could be going wrong? Where do I start debugging this problem?
Yesterday I took out all the cards and the hard disks and with only the
two CD-ROMs connected (because I couldn't disconnect their power cables
easily) I switched ON it's power supply and the same behaviour occured.
No boot at all. Just the flickering power LED and the CPU fan whirring.

->HS

 

Try another ATX power supply ? The power supply is the most
unreliable thing in a computer, so try another one. The
flickering of the mobo green LED, could means there is
something wrong with the power supply +5VSB output.

HTH,
Paul