The PSU is looking like it has issues and possibly caused by it`s age/usage, they have a life expectancy and are normally covered by a set amount of time period warranty or a MTBF (mean time between failures) such as 100,000 hours, please see my canned text below;
As a PSU puts out various voltages +3.3V, +5V and +12V it may appear that the PSU is working correctly but it is not, any significant drop of any output can prevent the system from booting up, the other scenario is a significant increase in the output which can be worse as it can fry one or more major components such as the MB, CPU, Ram, add on video card etc.
Please be aware that there are no user replaceable parts in a PSU so a bad one should be disposed of in a responsible manner and any type of conclusive testing will need to be done by a suitably trained Tech who has the required testing equipment and the relevant knowledge as to how to use it.