I've solved the problem myself, learning a bit in the process and putting some nitpicks into evga software.
 
The culprit was (most probably) a failed bios update (which probably didn't ask for my consent to be installed, but I can't be sure, as I've noted, the bios update popup goes regularly up regularly, and without newer bios installed).
Still, it probably gimped the leds and LCD. 
 
SOLUTION. I've removed the Unleash RGB software form my PC. (it didn't see the KB anyway).
I've installed the oldest available version (1.0.1.0) from the drivers page, and bam - it has deduced that in fact, there is a keyboard with unknown bios connected. It asked me to flash it, which i did, getting some old bios version. (1.13? not sure, don't quote me on that). Then I made factory reset (through unleashed options), and flashed in again, getting 1.16 bios. 
Uninstalled Unleash, and installed it again with newest version (1.0.6.0). It has now recognized the Z10, and, guess, flashed it, getting to 1.17. 
Working stable ever since.
 
So, in a nutshell - EVGA, please:
- check the compatibility triggers in your software - it is  baffling why an old version recognizes the blanked device, while the newest does not.
- check the factory reset packages that are connected to the FAQ about z10 LCD - they didn't recognize the keyboard at all, nor they recognize it now. Outdated versions? Bad IDs?
- check the flashing utility in unleash RGB - as i've observed it sometimes reports the bios version as 0.00 and tries to flash it, which as we can see has a chance of breaking the device. It happens most often when the z10 is disconnected and then connected again. (I'm using KVM)
 
Hopefully it will help someone with a similar case of bricked (well, technically blacked out) z10 ;)