First I'll mention the obvious. Sounds like you have a pretty b0rked install.
Secondly, is there any particular reason you haven't reinstalled yet? A person can spend hours on hit and miss or reinstall the system which usually takes about 20 min. which will give you a nice, clean, stable system.
Judging from the posts here, I am afraid you are kicking a dead horse.
Now as I understand this happened after a major update, this is not unheard of. It is very easy to nuke a Debian install if you don't follow some basic rules which should be stressed a bit more on this board, they do so in the Debian forums and they know better than anybody else since it's their system. They do not make their recommendations to be arbitrary, they have a great deal of experience. Remember this is Debian it is not Ubuntu or mainstream Mint.
That being said, here is the proper way to do a major upgrade of a Debian system adapted to Mint. I will try to explain the whys briefly.
1. After you have completed a clean install and rebooted, create a root password.
#your new root password
#your new root password(again)
2. Log out. While at the gdm screen press ctrl + alt + F1. This will bring you to a cli login prompt. Login as root.
3. Go to runlevel 3
(you may have to press <enter> once.)
this will completely unload the graphical environment's modules. this makes a major upgrade much, much safer.
4. refresh the apt cache.
5. start the update.
after everything downloads and the upgrades commence take note of any warnings. the information can prove invaluable if anything goes wrong.
6.after the update completes.
Now hopefully this will take you to a nice clean, freshly updated system.
Some "do nots," NEVER use Ubuntu repos, avoid using graphical package managers if there is any danger of it trying to overwrite loaded modules -- sometimes it works, sometimes it doesn't. It's a crap shot. When in doubt, it's always better to err on the side of caution. Do not mix testing and Sid repos, you might see some here doing that for selected apps but it's always a gamble.
Write your password(s) down someplace. at least right at first. especially if you use strong passwords as they can be the devil to remember. (btw, I'm not suggesting that was the case here but it's still wise, especially if you use complex passwords.)Read the release notes, Clem's blogs about LMDE and the Debian documentation.
Understand the skill set required to properly maintain a Debian system. Read and learn. This ain't Ubuntu, it's a development branch of Debian. Because Clem has provided some handy tools, a pretty default interface and a really slick installer and also because things are usually pretty trouble free it's easy to lapse into that mindset.
If you treat your system right, it will be with you for a very long time and as you learn how to do things you will find it provides more power and freedom than Ubuntu or Ubuntu respins.