Hi Islevegan ,
There could be many possible devices that are causing the problem, such as a defective NUC, a defective power adapter, power cord, etc.
My recommendation will be to make sure the power adapter is working fine and the power cord as well.
Try the system with minimal configuration (NUC, power adapter, 1 memory stick) Check for lights, fan activity
If you continue having the same behavior, feel free to contact your local Intel support group for assistance on replacing your product : http://www.intel.com/p/en_US/support/contactsupport?group=process
Regards.