There are only two ways to test a PSU, and since you've got a multimeter, I recommend you use the multimeter test. The other test, a far less accurate method, is simply jumping the green wire with a neighboring black wire. This test can provide false positives, in that if the PSU turns on, some believe this to be an indication of proper operation.
Using the multimeter, touch the black lead against any black wire, or bare metal on the case. Touch the red lead to the following wires, and verify their voltages, while the computer is powered on:
Red = +5V
Yellow = +12V
Orange = +3.3V
Blue = -12V
Green = +5V
Purple = +5V
Brown = +3.3V
Gray should go from 0 to +5V when you turn on the case switch
I think this is the way to go. Although the other suggestion of swapping out PSU isn't bad I think Ill use the multimeter to be sure. I hope the MOBO is dead so I have an excuse to build him a new PC and stop having to troubleshoot these old relics but as a builder of Pc's myself I still want to know what exactly the problem is. Thanks.