Is the Memory in the bottom slot? If you installed two RAM Modules, try each module on its own in the top slot and bottom slot.
If you remove the SSD does it display the Intel NUC logo?
If you remove all USB devices and anything else external (except monitor), does it boot?
If still no luck, you could try reflashing/updating the BIOS using the jumper technique. Try the power button technique as well.
Instructions are in the PDF on the page where the BIOS is downloaded from.
I was able finally get video on on a VGA monitor. The first 3 monitors I tried on were blank (2 VGA, 1 HDMI).
Firmware was 042, so immediately updated everything. I didn't try on HDMI, but the vga monitors all work now.