So, I demanded a tech be sent, and send a tech they did with a new Motherboard, and power supply.
He had to come to my store to do the repair, as I work all day and couldn't meet him at my home. He was in the back for a few minutes before there was a loud pop. Apparently something sparked, there was smoke, and the PC was still dead.
He called it in, and Alienware told him they would contact me in 24 to 48 hours. Ha. Ha. ha.
I called them right back. They decided, after putting me on hold for a long time, that they would send the tech another motherboard and another power supply, as well as a new video card, liquid cooling system, and some various daughterboards.
The tech showed up the next day, which I was not expecting. He managed to get the PC up and running by replacing the power supply, motherboard, and video card. (Which was only 2 weeks old anyway, but...whatever.)
So, I had the long holiday weekend off and managed to play Guild Wars 2 for a long time. It seems like the PC is running well now, but I'm a little afraid something else will die soon. I'm actually contemplating replacing the OS hard drive with a SSD to make it A) Faster and B) a little more stable. (I had to do an Alien-respawn because the drive created bad sectors over some important OS files...) But, we shall see.
Bottom line so far? If you are going to shell out money for an Alienware, make sure you spring for the extended warranty and coverage. This one would be a paperweight a little after a year since purchase, and that's not good for such an expensive desktop. I'm not knocking Alienware. I used to work in IT and I know what a crapshoot PC hardware can be. I'm just saying that you'd be better off following the safe path. You're dropping over a grand, you might as well go all in, right?