There seems to be 100 ways to test the powersupply. Both in the wall socket and in the PC. The easy and obvious way to test this is to connect a different PC to the wall at the same socket that is used for the difficult PC. Connecting a lamp to the wall socket is not going to tell you anything. The glitch is likely to be to short to notice.
But if you have clients buying PCs from you, it can't be a big deal for you to get hold of a UPS. To my knowledge a UPS is a box that you can charge and that will provide great sinus waves even 5 mins after power is terminated.
Btw, have you been to your clients location? I had a PC that acted a bit like this once. At first we thought it had some connection with the tram lines outside in the street creating interference on the power grid. But it turned out to be a faulty soldering on the hard disc. Problems like these nearly always are related to soldering. Have you tried replacing the motherboard and discs?
It seems to puzzle you that it worked for a year before problems appeared. It does not puzzle me. It can be caused by many factors. Lightning (VERY COMMON), sudden glitches in power supply, dust between the processors fan and colling ribs, a weak soldering combined with any of the above can cause probs like this. I Norway where I live we have a law that says you can go back with stuff to the shop for 2 full years with anything electrical. It has proved quite efective cause many appliances have a tendency to break down after just over a years use.
Heres a quick run down of what I would have tried:
Connect a UPS between the PC and the wall.
Get hold of a new power cable.
Rip out all extension cards.
Put in a hard drive you know work.
IF need be: test all components in a controlled environment
Try the motherboard in a different cabinet.
I assume you have done al this, so when you are sure everything works theres only incompatibility issues and soldering issues left. Now, incompatibility does in general not take a year to show up, so its likely tyo be the latter. But remember, putting the motherboard into another cabinet is not going to tell you anything if you just leave it there. You'll have to find some way to stress it. Try some extensive benchmarking.... Btw, have you asked what your client was doing at the exact time of the crashes.
Furthermore I am not too surprised by the fact that it turns it self back on again. If its a faulty soldering, this is quite normal. Think about it.... as it gets warm it looses connection... whats to say it can't regain that conn after it gets cold again? Most my computers boot when I turn the power on....
Suggestions for further inquiries:
Move the PC around the house to make sure theres no interference problems.
Try a different house with different powergrid.
Find out what PC is used for when it crashes.
If this is a one year old PC it should have temperature section in the bios. If this is ok, you can assume that processor heat is not the cause. But thats not to say the problem is not in the processor.