"GNOME System Log" is just a log viewer, by default in Trisquel (not Mini).
Assuming it really is installed on your system, you can launch it from the
terminal or from the Alt+F2 prompt:
$ gnome-system-log
LightDM is Trisquel's default display manager. It is automatically launched
when the system starts. I was just telling you that you need not reboot when
the screen gets scrambled. You can just restart the graphical session with
the following command, which you can execute from a text session (such as the
one you get with Ctrl+Alt+F1):
$ sudo restart lightdm
But, before that, you could copy some logs (if there is anything interesting
there, it is probably written when the screen gets scrambled). And you could
take a look at whether a process is guilty of using much CPU and/or memory:
$ top
