Try to open a terminal with
ctrl + alt + F1. Then you can mess around with the unity greeter, ubuntu-desktop and your graphic drivers.
Some of the answers here might help in your case: How to fix "The system is running in low-graphics mode" error?
You may try:
sudo apt-get install --reinstall ubuntu-desktop or
- this anwser
If really stuck, backup your files and reinstall. It may help to locate the update that causes the problem. (I empathize: I am myself in this situation where I am almost certain that a update/reboot would crash my computer. My model is Samsung series 9)
In my case, the likely update is the unity-greeter update tough I am not sure. My symptom is that I am unable to login (even with correct password, the login screen reapears). If I boot in failsafe, I get "System running in low graphics mode".
Procedure for backing up your files: (in the terminal that you access with
$ # Insert flash drive
$ ls /dev/sd*
$ sudo mkdir /mount
$ sudo mount /dev/sdb1 # maybe sdc1, sdd1...
$ sudo cp -R /home/yourname/ /mount/
$ sudo umount /dev/scb1
$ # remove flash drive and check your files on another computer
$ # reinstall