Dell XPS 12 :: Won't Start / Power Up After Hard Reset

Last night I was using my XPS w12 in laptop mode on battery and it finally got down to 7% of capacity.  At that point it shut off the screen and I moved to my office to connect the AC adapter (thinking that it would simply turn the screen on when there was sufficient power. .  The screen never came back (I waited 15-20 minutes) but the battery was charging.  At that point I attempted a hard reset by holding the power button in the on position for 5-10 seconds. 

When I tried to power up, nothing happened.  No backlit keyboard, no screen, nothing but the fan.  The light never came on in the switch either. So I tried another hard reset with the same results.  I even tried powering up with the "D" key held down for on board diagnostics and got nothing but the fan startup.

I thought it might be an overheat issue so I let it set for an hour and tried again - nothing but the fan. It appears that the laptop doesn't pass the initial diagnostics and won't even get to the point where the bios starts to load. 

 I truly thought my laptop was dead and ready for service.  I took it into the office the next day so I could call Dell Pro Support. Just  for giggles, I plugged it in with the AC adapter and tried to turn it on - viola!  it started working again.

I had this problem once before and it started working after 2-3 hard resets. I was working on a proposal when the laptop went down. I tried hard resets over a 4 hour period with no results. It baffles me why it would start OK the next morning.

I'm running the A07 BIOS (the most current) and my XPS 12 is configured with 8GB of memory and 256GB SSD with an i7 processor and Intel wireless card. The hard part is when if fails, the failure is total - you can't get to the diagnostics. When it comes back everything is fine and there are no events in the event log that relate to the failure.