Not that it might help you but BIOS 35 worked fine for me using:
NUC: D54250WYK (i5-4250U)
Memory: Kingston HyperX Impact Black SO-DIMM DDR3 PC12800/1600MHz CL9 LV 2x8GB (HX316LS9IBK2/16)
Harddrive: Samsung 850 Pro 1TB
Chassi: Akasa Newton X
Thermal compound: Arctic Cooling MX-4
Monitor: Eizo S2231WSE
Cable: Deltaco mini DisplayPort to DVI-D, male-male, DP-DVI202
Keyboard: Logitech K120
Mouse: Logitech G400
OS: Ubuntu 14.10
In BIOS I have disabled secondary display and forced primary display to use mini-displayport. Also set the video memory setting (forgot its name) to 1GB.
I think what you see is the incompatibility caused by Intel altering how the BIOS will be displayed after around BIOS 27 or so.
Previously the BIOS screen was full screen (sending out (I think) a 1024x768 signal) but then they changed this so the BIOS screen will be a 1024x768 window within whatever native size is detected by the NUC during boot (for example if 1920x1080 is detected then it will send out a 1920x1080 signal with the BIOS screen centered using 1024x768 with black borders).
This caused that a lot of us running various cable converters (since we dont have monitors with mini-displayport or hdmi as input) ends up with garbled screens because the NUC incorrectly detects which native resolution the monitor might use due to the cable converter.
If this is the case for you, does it mean that before the update the BIOS screen was full screen for you?
That is what version did you use before your update into BIOS 35?
This is a very strange behavior. Honestly I have flashed some NUCs these passed days and have been working just fine so I would say something went wrong during the flash process.
I recommend you doing the recovery to the same version you installed. Here you have the steps:
You can also try flashing the BIOS with another version:
If re-flashing the BIOS on the system is not working and you have tested different steps I would say you should contact our phone/email support for them to check this and provide a replacement if necessary.
Here is the contact information: