"Additionally, my UPS sometimes makes a clicking sound before the restarts. Again the power supply has been changed."
Using that as the big clue, I would supersize that power supply. If it was 350 Watts I'd try some 700 Watt model. The UPS dipping out is the big clue here. Your PC is just suffering a loss of AC so there is nothing truly wrong here with the PC. But by supersizing the PSU in the PC you can effectively give it some a little more time it will survive without AC.
Another owner discovered it was the UPS. The reboots stopped when the UPS was removed from the system.
Simple. The computer just suddenly decides to do arestart. I've been through every possible scenario and tested the memory, processor temperature, hard drives for faults with their manufacturers' software, bought a new power supply... no, it just still does it. Perhaps the strangest thing about these restarts is their frequency. They're rare, about once a month. And they do not seem correlated with any hardware or software activity that was going on at the time.
Windows is set not to restart if it encounters a BSOD so I'm really out of ideas. I've eliminatd any software causes such as updates requiring restart, viruses and so on. So what DO I know? I know only one thing. When my computer restarts, it does a short beep. Now I'm sure many of our computers beep on startup, as does mine, but this one ONLY beeps on startup if:
-it is starting up from power-off mode
-its BIOS had been configged and a restart is required to apply them
-you push the restart button on the case
A restart from inside the OS or one caused by a BSOD will not make it beep. Additionally, my UPS sometimes makes a clicking sound before the restarts. Again the power supply has been changed.