Thanks to everyone for the hugs and words of encouragement. After lunch things did calm down a bit and my headache finally went away (lending credence to the theory that it was a blood sugar problem).
Also in good news, I picked up a new 500w power supply at Micro Centre while I was out at lunch, and installed it when I got home. It definitely turned out to be the problem, as my system sprang to life immediately after this swap was made.
Tomorrow will be a long day, but I dare hope it will be a better one. 🙂