Can you try the commands (excluding lightdm) in the solution here?
Specifically,
sudo apt-get remove plymouth
sudo apt-get remove xserver-xorg-video-intel
But then branch off to the following, if you see the dark screen after logging in:
Ctrl+Alt+Fn3 (for you it could be anywhere from Fn2-Fn6, for me it is Function key 3). In the terminal that now appears, type sudo apt install ubuntu-desktop. Then reboot. Then sudo apt install xserver-xorg-video-intel. Then reboot.
I can’t remove because there is not installed and I can’t install because I have held broken packages
Do you have any personal files you need to backup? I’m thinking a OS reinstall may be quicker.
If you choose to reinstall, as long as you don’t select format for your Home partition during installation (“Something Else” installation option will take you to the partitions), your files on Home will be preserved. After reinstall it then appears as a separate volume to mount and access.
Otherwise, we can try to keep troubleshooting. This time, we would select the dpkg option in the recovery menu.
I’ll leave the choice to you.
I think I’ll simply reinstall the OS, I have 2 storages so I don’t need to backup my files and it’s a little bit late here (1AM). I think I just had a rare bug, we tried and it didn’t succed, it happens sometimes.
But really thank you for your help, maybe one day it’ll be fixed in an update! 
Sounds good - I do the same, I have 2 storages that are separate from the OS. Sorry we couldn’t resolve it and sorry for keeping you late.
If you’re interested, when you reinstall, these are the partitions I recommend: Partitioning during installation