First, you may have something wrong with the case power switch. If, instead of pressing the motherboard switch, what happens when you try to turn on the computer by temporarily shorting the PSU green wire to ground? If the system starts, you have a problem with the case switch.
Alternately, you can swap the case power and reset switches and try to boot with the reset switch.
Second, like henydiah suggests, you may have a problem with the PSU.