You can check system logs after reboot with: sudo journalctl -b -1 where -1 stands for previous boot (-2 for one boot before previous boot, etc). Maybe it will show some hints about what happened with your system before laptop reboot.
If there is no error messages in the logs, then it is definitely a hardware problem. And since you bought used mobo it could be anything, from bad soldering to faulty controller that was overheated during repair procedures. >From my experience, I'd suggest you swap mobos to the one you bought laptop with( with nvidia GPU on it ). Power consumption and hibernate\resume won't be an issue because you can use integrated graphics adapter from your CPU and use nvidia GPU only on demand via primus\bumblebee.