A total system freeze is likely a hardware issue and not software. If you have a bootable USB drive, try creating a portable Linux and booting from it. If it too, freezes, you'll know it's hardware-related.
Could it just be the graphics (X11) that's frozen? Try pressing CTRL+ALT+F4 to switch to a console. If it's out of memory (RAM), it could take minutes before it responds. The disk activity light may be illuminated (if your desktop has one)
Consider adding the System Monitor applets to your MATE panel so you can see the graphs if they fill up at the time it freezes up.
D-Sub port, supporting a maximum resolution of 1920x1200
1 x HDMI port, supporting a maximum resolution of 4096x2160 * The resolution of 4096x2160 can be supported when using an FM2+ APU; the maximum resolution supported is 1920x1200 when using an FM2 APU.
After it locks and you have restarted, you could open a terminal and look at the system journal to check for any warnings or errors that preceded the lock e.g.:
journalctl -b -1 -n 20 -p 4
Explanation:
-b -1: show entries from boot with ID '-1', i.e. previous boot.
-n 20: show 20 lines (will show last 20 lines).
-p 4: show entries with at least 'warning' priority or higher (e.g. errors, fatal etc).
Most of the time, this doesn't show anything useful (because the error stops the log anyway) - but you never know your luck!
I suspect you won't find much information here either, but you can try the dmesg process for reading the Linux kernel ring buffer. If you want to only display errors, use dmesg --level=err. Read the manual pages for more information man dmesg.
The little button on the case will be the RESET switch. It's a soft restart button, so kind of like powering it off then on again.
Another idea to figure out why it's freezing could be to set up an SSH server and log in to your desktop from another system (a laptop or tablet).
From a terminal logged in to your main computer, run sudo dmesg -w to keep printing the kernel buffer until the system freezes. If you run htop in a second instance, you'll be able to observe the last processes and memory/swap usage.