I generally just yank the motherboard, CPU and memory, and often the power supply, and replace them with another set (I just don't have time to screw around). The problem often goes away after this.

We then use the parts internally to confirm if they have problems or not. The amazing thing is how many times no problems crop up and the parts give years of flawless service, especially if they are dispursed separately, but in some cases the whole set has run just fine. I ascribe this to slightly different power supply voltages or other things that influence internal timing.

This is actually the mechanism by which some of my machines gets upgraded (the rest are upgraded with stuff stripped out of client machines we rebuilt to run latest Microsoft bloatware).

Power supplies, by the way, are the last thing people think of, but are a prime cause of flakiness and instability. They may be off voltage, noisy, or poorly regulated. Shopping for the lowest price in a power supply is a recipe for endless problems.