There are two ways of going about testing the power supply.. You can swap in a supply of equal or greater wattage and if the problems go away, then you've found the culprit. If problems persist, then the board is likely the problem.
The other way is finding a voltmeter and testing the psu directly. If the values measured fall within +/- 5% of the voltages specified then you know the psu is the culprit..
See here for the break down of the voltage pinout of the psu..
http://en.wikipedia.org/wiki/ATXDon't bother with the negative voltages
edit: make sure the computer is on, if you decide to test the voltages with a voltmeter