New Aurora R4 needs to be booted twice every time

I have a new (“certified refurbished”) Alienware Aurora R4 with Windows 8 Pro which has an “out of the box” issue – after powering down properly using the “settings” menu, when I turn on the computer the next day, I have to do so TWICE. The first time I get the “Alienware” screen underneath which a progress bar pops up for a few seconds showing it’s an Alienware computer using  BIOS A07; this disappears and is replaced by a pattern of five dots that start revolving in a small circle; their revolution stops almost instantly and the screen goes blank and stays blank, even though the lighting effects on the PC go on and the disc drive is active. There’s NO error message or BSOD; during this process the computer beeps once.

If I then turn off the computer by holding down the computer’s power switch, the PC goes down . . . if I wait 10 seconds and power back up, I get the logo, BIOS bar, and spinning dots, and the computer goes to the Win8 splash screen. Enter password, and the PC behaves normally all day no matter what I do.

I ran Dell’s ePSA test and the PC passed with no errors. (The last part of the test took a couple of hours!)  I uninstalled the trial McAfee antivirus and installed Kaspersky 3.0 with no change in the PC’s behavior; updated Windows from the Microsoft website with no changes in PC behavior; enabled SLI from the Nvidia control panel (dual GTX680 cards) with, you guessed it, no change in PC behavior. The PC is plugged into the monitor (primary card!) via HDMI, and there are no peripherals attached other than DSL modem, mouse, and keyboard. The PC has two, 2TB drives that are discrete – no RAID array, no SSD.

I'm guessing it's a BIOS issue, but I don't know enough of its workings to go blindly poking around. So I'm looking for suggestions – a pricey PC like this shouldn’t have to be booted twice.