I’m on the computer for now. It turned out that the inner fan of the power supply had seized up. The power supply was spending so much time working to move the fan that it started to overheat.
Jason luckily found a replacement. So he disassembled the power supply and replaced the dead one. Unfortunately, he won’t put my graphics card back in for at least an hour to make sure the computer itself can stay running. So far so good, knock on wood. It’s been running for a total of 5 minutes already. Power supply is still cool to the touch and the computer (obviously) is still running.