PC keeps restarting randomly

Every single time I try to install a new game or run a software installer, my computer just gives up and restarts itself... it's even happening when I'm simply moving files over to a USB drive! Once the machine finally boots back up, I'm greeted with that dreaded message: "The system has recovered from a serious error."

OS: macOS SP3
RAM: 1.5GB
Processor: 2.0GHz
HDD: 60GB

I've already gone through the motions of checking the processor temperatures and the health of the hard drive, and everything seems to be running perfectly within normal limits.

I also just finished doing a completely fresh installation of the OS.

Anything is possible... but first, check if the power supply is still holding up.
The PSU is what draws the most power... the 12V rail is the one you really need to watch.
There are plenty of UEFI versions and motherboards that display voltage levels directly in the UEFI.
Alternatively, put a multimeter on a yellow wire from the power supply against the case chassis... it needs to be at least 11.40 volts.

Good luck.