-Is the Power Led illuminated when you switch the unit ON?
-Can you try other video cable and/or other video input in monitor (i.e. Display Port or HDMI)?
-If you don't see any video output at all (even not an Intel logo during boot), try to recover your bios: BIOS Recovery Update Instructions for Intel® NUC and
Hope this helps
For the most part, I agree with Leon. My prioritized list of things you should try is as follows:
- Perform a CMOS reset. This is detailed here: Intel NUC Clearing CMOS.
- Perform a BIOS recovery using the latest available BIOS. This is detailed here: Intel NUC BIOS Recovery Update Instructions. Leon's link to video showing process is good too.