Go on ebay and buy a 3 pin to 4 pin fan adapter, or you might find one locally. Then you could plug it directly into a standard molex plug.
If the fan and the cabling is ok, then this should work fine. There is a case though that the fan or the fan cable are shorting out somewhere. In that case i would not recommend connecting it to any power supply unless you get it fixed or throw it away and buy a new one. That is one explanation why your motherboard is not booting. Other explanations are:
1) That motherboard header or all of them cannot provide enough power to power up the fan, hence the system will not boot at all, since none of the fans are spinning.
2) The fan control chip on the motherboard is faulty, hence when you connect something on the header, it immediately shorts out and prevents the system from booting.