Issues with Alienware X51 R3

Hello,

I purchased an Alienware X51 R3 (i5-6600K, 8GB DDR4, 1TB HDD, GTX 745 4GB DDR3).  It arrived today, and I noticed a problem:

I've updated Windows 10 Home, since then the machine boots, but has a black screen.  Sometimes cold restarts or unplugging the power cable for 30 seconds will result in booting to the desktop, but most times it doesn't.

Updated the GPU drivers, same thing.  Took out the 745, used the onboard HDMI... Same thing.  Tried the Win+P three times + Enter suggestion... Guess what? Same thing.

I've updated the BIOS to the latest revision too.

Any ideas what's going on, and how to fix this? It's driving me crackers that I have a machine I can't game one (OR USE!).