I am not from Intel, but there seem to be two common problems. One is are you perhaps trying to hook to a computer monitor rather than an HDTV? When my NUC was delivered it would not display on computer monitor, but would display on 1080 HDTV. After updating the BIOS (which involved using a non-Microsoft keyboard), I was able to display on both a computer display and an HDTV (although the display may be forced to 1024x768@60Hz in center of screen).
The other common problem is that just saying 4GB 1.35v is not enough detail. The 1.35v needs to be specified in the SPD using JEDEC standard (probably is), the chips need to be of a certain "density" (not sure but this probably means only 4 or 8 chips per side not 16 chips per side) and the speed of the memory probably cannot exceed 1600. Incorrect memory may produce some blinking pattern on the power light (again, not sure about that detail).
Hello Clarkie42, thanks for joining the NUC community.
I would recommend you to perform a BIOS update using the recovery procedure.
If the behavior persisted please contact Intel support for warranty options at:
Online warranty: New Service Request
Chat support: Contact Support