There is such a thing as doa in electronics, not saying that you have a bad cpu but do not rule it out.
Also depending on what is plugged into your motherboard dictates how much power you need, ie; hard drives,fans,video cards etc.
If you want a basic estimate on wattage required here is one site you can try.
eXtreme Power Supply Calculator
This is not an etched in stone figure,if your MOBO is older than the new processer factor in also slightly more draw.
once you know that your power supply is adequate then you can fault find your cpu issue.
If this is the original power supply then factor in about a 10% loss in efficiency per year of use, if you are a heavy user (on all the time).
hope this helps