What happens here is that you have a system that is half-upgraded and got interrupted. Alas, it makes it hard to login via the normal graphical login. That is no big problem, as long as you can get into your a shell (terminal) in order to kick off the upgrade again.
So, where can you find this shell? Most Linux installations offer you a text-only interface, totally separate from the graphical interface. You can typically get five different logins (called "consoles") and you access them by hitting
F5). To get back to the typical GUI interface, hit
Start off by hitting
F1. You now get presented by a text screen containing something like this:
Ubuntu 16.04.1 LTS my-machine-name tty1
At this point type your username and press enter. The following line will appear:
You now type the password of your username. It will look as if nothing is typed. There are no is no "echo" as it's called. You won't see
* or anything appear as you are used to in normal password fields. Press enter after you entered the password. You will get more text, like this:
Welcome to Ubuntu 16.04.1 LTS (GNU/Linux 4.4.0-34-generic x86_64)
* Documentation: https://help.ubuntu.com
* Management: https://landscape.canonical.com
* Support: https://ubuntu.com/advantage
4 packages can be updated.
4 updates are security updates.
Last login: Sat Aug 20 19:30:47 2016 from 192.168.2.4
This last line is your prompt. You can enter commands here, just like you do on the terminal application.
Let's kick off the update process again. Normally you start with "updating" the repositories. It's probably not necessary, but it's good practice to do so:
sudo apt-get update
At that point, we're ready to kick off the distribution upgrade again, which can be done by:
sudo apt-get dist-upgrade
You now have a lengthy process of package installations. It will ask questions: Just take the default answers. Especially if you don't understand the question.
After a while you return to the prompt. You can now reboot.
After reboot, everything should work again. If not, repeat the process until the
sudo apt-get dist-upgrade is not doing anything any more. This will look like this:
Reading package lists... Done
Building dependency tree
Reading state information... Done
Calculating upgrade... Done
0 to upgrade, 0 to newly install, 0 to remove and 0 not to upgrade.