Would you guess that Proxmox is more friendly with non-mainstream hardware? I will try to follow the ESXi compatability guide (thanks for the link!) for selecting the hardware and then experiment with Proxmox.

Thanks, tried that, however it made no difference. I also edited my question - it is possible that the NUC box actually booted into Windows but I simply had no picture on the screen. That combined with frozen HDD light gave me impression that the system is frozen.