To make sure the CPU wasn't setup improperly, I removed the heatsink to ascertain the model and speed, so that I could reconcile them with the model and speed the BIOS reported. The BIOS was correct, but to try a few more possible solutions, I cleared the BIOS, reset the BIOS to failsafe defaults, and re-flashed the BIOS. Rebooting after each of those steps, I encountered the same problem. This was not unexpected, however, because the likelihood of a CPU failing is pretty low. The only thing left now was the motherboard.
To make sure there wasn't a short-circuit anywhere, I cleaned out all the dust in the computer, and removed the motherboard from the chassis. Then, I tested the problem using original components as well as my own components (repeating several of the above steps), and it was still there. I even tried Knoppix again, and this time it completely loaded, only to reboot while the computer idled at the desktop. It was now logical to conclude that the motherboard was faulty.
Because the reboots happened intermittently, the exact cause of the problem is difficult to ascertain. Reboots occurred during Windows startup, while Windows was running (as my aunt reported), and when setup began its graphical phase. With Linux, the computer just froze during startup, and rebooted randomly when the OS was running. Since I don't have a spare motherboard and CPU to test with, I cannot determine with confidence that the motherboard is the problem. On the other hand, I have tested every component other than the motherboard, and if you remember that one of the two most important things to do while troubleshooting is to maintain a logical attitude, then you will realize that we have eliminated the impossible, and only the motherboard remains. I replaced every other part of the computer with known working parts, and the problem still occurred. This implies that the parts replaced were not causing the random reboots.
As I mentioned at the beginning of this story, troubleshooting is a tricky task. Troubleshooting is like a mystery that you must solve, with a trail of clues for you to follow along the way. Thus, we use logic and document our results as we proceed. We swap out parts, trying to determine if one is faulty. We run tests that stress certain components to determine if those components have failed. In the end, once we have eliminated all other possible solutions, once we have burned away all the hay, we arrive at one conclusion: our needle.