Good news: your RAM is OK. If it was not, the screen would have turned red.
Memtest86+ starts over after doing all its tests: you can terminate it now.
Let us now see if the disk is OK. Trisquel has, by default, a tool named
"Disks" in the "System Settings". In it, you can select a disk (left-hand
side of the interface), click the button with the gear icon (top-right
corner) and choose "SMART Data & Self-Tests...". You can then "Start
Self-test" (button in the bottom-left corner) and choose an "Extended" test.
At the end, the "Overall assessment" will tell you whether the "Disk is OK".
If it is not, you had better backup your data asap and very regularly do so
(anyway, all users should regularly backup their data).
However, I doubt that errors in reading data on the disk would result in a
scrambled screen. If the problem comes from the software, there may be
something interesting to read in the logs. Those logs are files in /var/log.
They can be read with any text editor (or, from a terminal, with 'less') or,
more comfortably, with the "GNOME System Log" tool (by default in Trisquel
but not in Trisquel Mini). Let us first see what errors Xorg (the graphical
server) reports, i.e., the output of this command:
$ grep '(EE)' /var/log/Xorg.0.log
If the screen gets scrambled, it would be interesting to read the end of the
logs after it happens. Without exiting the session (or rebooting the
computer) first. To get a (real) terminal, type Ctrl+Alt+F1. It should always
work. Even if the display of the graphical session has become unreadable.
Enter your user name and your password and copy the Xorg log in this way
(here to a file named "EE.log") that you can then attach to a post on this
$ cp /var/log/Xorg.0.log EE.log
To get back to the graphical session, type Alt+F7. By the way, would that
unscramble the screen? If so, we have a fix! If not, there is no need to
reboot. Here is how to restart the whole graphical stack from the terminal
(again, you can get one with Ctrl+Alt+F1):
$ sudo restart lightdm
I assume here that you use LightDM, which is both Trisquel's and Trisquel
Mini's default display manager. Of course the work you were achieving in the
graphical session should be first saved... if possible!