Yep, should have been more clear--the PSU is what you can test with a multimeter, for sure. If you get fancy, you could see if power is getting to different parts of the motherboard, but considering the near impossibility of fixing a four or six layer motherboard in the field, it's not likely to be a very fruitful line of investigation.
As far as motherboard testing goes, you can really only test with another computer of a similar build, or a similar bunch of parts, and a large amount of patience.
Kevin's got a great point too--you can get a nice PSU for well under a hundred bucks--either it fixes your problem, or it eliminates a new one when you buy that new computer with a junky power supply--and you switch it for the good one you bought.