As I speak, freshly-built computer has only two fans spinning: the power supply fan, and the CPU fan. The harddrive is an SSD.
Putting my ear up to the power supply, the sound is clearly not coming from it. It's whirring nearly silently.
Putting my ear up to the CPU area, however, lead me to believe that the sound was coming from the CPU fan. I replaced it, and the sound continued. So, on the new fan, I put my finger on the middle of the spinning fan until it stopped (the temps were fine afterward!), and the sound was still there.
Can CPUs themselves make noise? This sound is catastrophically annoying. What could it be?