You can't really unless you have a spare psu. Unless you have specialised testing equipment, testing a PSU is very hit and miss.
Try and run the pc with the absolute minimum of components. Motherboard, CPU (stock), 1 stick of ram, basic GPU and single hard drive. This is to put the minimum of stress on the PSU. Perform a clean install to eradicate the possibility of driver/OS issues. Only install the drivers for the hardware you have installed then perform a few basic tasks.
It's basicly a process of elimination I'm afraid when troubleshooting. Start off with the basics then add one component at a time to see if you can pinpoint the problem. In your case I had similar issues which was indeed a PSU problem.
I was afraid you might say that!

I've just performed a clean install within the last week though. I installed only the essentials and it has the same errors, more or less.

Only thing is that although I tried a single stick of RAM for gaming, and performance was still crap, I didn't keep it in long enough to see if it caused the other problems I've had. I think I will give the system a long run with 1 stick and see what happen.
It could well be that the poor game performance in these games is normal for Vista 64, and the other issues are unrelated.
I will try 1 stick, then a full reinstall of XP (on the most basic setup as you described), and if both of those fail then I don't know!


