I got a response from Xbox email support saying they would work with me to replace the power supply, but I had to call the support line. I did, gave my info to another Indian gentleman, who then transferred me to an American-sounding gentleman ("Live support", he called it). He told me that I had to send the power supply in before receiving a replacement, which would leave me without the console for who knows how many weeks, with an expiring Xbox Live subscription. He wouldn't agree to send me a new unit first, and I even offered to give a credit card as collateral against them receiving my faulty unit back. But he couldn't/wouldn't offer me any other options.
So I asked to speak to a supervisor. I waited on hold for 45 minutes with that terrible, terrible techno music playing. I almost took my own life. Just in time, I removed the razor blade from my wrist when the supervisor lady finally came on the line, but she wouldn't work with me either. So I was told to send the PS back to here:
5700 S Industrial Parkway
McAllen, TX 78503
So I have to figure out a time when I want to be without the Xbox for a while. Sigh.