This happened to me just a few days ago. I'm glad this story was put up... I'm not convinced it's "social engineering" or "phishing" as EA/Microsoft are eager to think. My Live account has been inactive for some time (which is lucky, I was only outed a couple hundred points that were leftover on my account since my credit card on file had expired). I definitely haven't had any phishing attempts in my email, I've never shared my account information with anyone, my Live password is unique... To me, it seems that there's some kind of exploit that is being used.
I've had experiences with 'flaky' power supplies. Not personally, but with people I've helped out. I think your problem could very well be with the power supply. At the very least, it would be worth getting a new one and trying it out as they're fairly cheap.