Does the computer shutdown out of the blue with no warning or error message's ? With the symptoms of intermittent shutdowns during idle,load and booting it does sound like your typical PSU problem. It's very common during a build for the PSU to be overlooked but when in fact it's actually a very important part not to cheap out on which brings me to my next question: What brand power supply is it ?
Unfortunately trying to determine if a power supply is bad and going off voltage readings via software is unreliable. The proper way to troubleshoot it is with a digital multimeter(DMM) if you have one and if you don't they are relativity cheap to purchase.