Hhmmm, it is pretty rare for both DIMMs to fail at the same time. This would more likely be an SOC failure in the memory controller or some other related component on the motherboard. I would be contacting Intel Customer Support regarding a replacement unit...
Yes it really looks like board's problem....as 1st check if there's no dust or some small dirt in RAM pins on motherboard. Then place both RAM modules (check also their PINs if are clean) there and enter BIOS to check how many GB of RAM it shows....maybe in BIOS you can run some RAM test....so check it. I also recommend reset BIOS via on-board PINs. That's all what you can do from your side
I suggest you to reset BIOS settings to default then, get into the BIOS and verify if memories are running at DDR3L-1333/1600 at 1.35V. and processor at 3.1GHz.
BIOS update might improve your NUC performance, the latest version is 0354.
The latest Chipset and Management Engine drivers are in the link below: