I believe that icon screen is provided by plymouth. It's supposed to be user-friendly but it certainly isn't friendly when something goes wrong and you can't see any kernel messages!
I found a Mint thread for restoring boot messages:
https://forums.linuxmint.com/viewtopic.php?t=384439.
istr that Debian used not to upgrade kernels but installed a new one alongside the old, accessible through GRUB's expert menu. If LMDE does that too, it would get you booted, but you'd still be none the wiser about what was wrong with the new kernel.
