When you press the power button on the front panel of your desktop board and nothing happens, one of the things you should check is the RTC oscillator circuit. If this circuit is not working properly the chipset won’t de-assert SLP_S3# signal and the computer won’t turn on. One easy way to check this is to press the front panel power button and then touch the 32.768 khz crystal pins with one finger. The electrostatic on your finger will induce clock pulses on the Pierce oscillator inside the chipset and the board will turn on. Be careful of not having too much electrostatic build up on your fingers; you could also a multi-meter on the ohm scale instead of your finger.
If this trick works on your dead board, it means the RTC clock circuit is faulty. You could try replace the crystal, the 10Mohms resistors, or use an external 32.768 khz clock oscillator IC. Hope it helps someone.