I have found that if you take a small capacitor (<10uf, 16V) and put the leads on the power button pins on the motherboard, it will power on the motherboard.
I took an old fan connector and pushed the legs of the cap into it, then pushed that assembly onto the pins.
You must take care to get the polarity correct on the motherboard. Take a multimeter, set for DC voltage, and with the motherboard plugged into the power supply, read the voltage on the pins. If you get a negative number, that means your positive lead is on the negative pin. A positive number means that the negative lead is on the negative pin. Make sure you orient the negative lead of the cap onto the negative pin.
The board *should* power up every time now. I've heard of people who didn't get this to work, so perhaps there are difference in boards that won't allow this. YMMV.