With the advent of the EPS (CPU power) connector and the PCI-e (graphics) connector, most computers no longer really need the "+4" part of the main power connector.
Most motherboards need no more than 4 or 5 amps at 5 volts and very little 12 volt power.
Having said the above, I think there is something wrong with either your motherboard or your PSU. One of my systems uses a GA-EP35 -DS3P and it doesn't care if it uses the 20 pin part of the main power connector or all 24 pins. Just checked.