If the issue of random shut down is a power supply problem...what is the cure? How can you determine what part of the power supply is at fault?

What difference would that make? I hope you don't intend to attempt servicing your PSU.

The cure is replacement. You can get a tester for under $20.00 Its a cheapie but it will tell you if it is working at all. Next is a voltage tester..... A real psu tester is going to set you back more than most people are willing to pay.

OK....I guess my question isn't clear. Let me be more specific. If the computer is randomly shutting down, and all over avenues for random shutdown have been eliminated then I guess it's the power supply. If the computer is hot to the touch when it shuts down...and using a powerful fan stops the shutdowns...then again guess it's the power supply that needs attention. The question is ...is it the adapter, the connector, or the power supply itself that needs replacment? If I take it to a tech it will cost me $150. just to find out. So, if there is a way for me to make this determination without that additional expense I would like to know. Will the tester that has been recommended identify all 3 areas? Thank you

Sounds more like a overheating problem. Check your temperatures in the bios. A power supply with a defective fan or one that is clogged up with dust bunnies that isn't allowing proper air flow through the power supply is a possibility.

yeah it sounds more like the PC is shutting itself down as a means of protecting itself from overheating. If there was a problem with your PSU, the reboots would persist regardless of whether or not you had a fan blowing on the case. If this is a vendor machine (and not one you built yourself), it's likely that a recent heat problem is due to dust accumulation (and less likely that the heat sink is poorly seated on the cpu). i would open the case, ground yourself (touch metal), and pull out all the gobs of dust bunnies you can find. then take a can of compressed air and use it to dust the heck out of this machine. Power Supplies are not user-serviceable, but if you stick the straw nozzle from the compressed air can through a slot in the PSU and give it a few bursts of air, you'll probably see plumes of dust release into the air.