I forgot to ask, what PSU are you using? Starting up Fallout 4 may be kicking your new card into a hungrier power-using mode and crashing your system because it is not being supplied with enough POWER. That card under load will still suck down a fair amount of juice, so it's a relevant question.
Other possible things to do if we decide that your PSU is strong enough for your video card: Test memory using Memtest86.org. Boot to USB drive is the easiest way IMO, or burn to CD.
Try using (www.Mersenne.org) Prime95 to run a stress test on your CPU. I use Speccy (click CPU) to monitor my CPU temps, but there are many programs that can. (Speccy can also tell you what voltages are going to your motherboard under the motherboard link, and to other components). You may also try HardwareMonitor from TechPowerUp.com. A few of their programs are useful.
Know what the max temp is for your CPU and keep an eye on it while you run Prime95. All cores will be burdened simultaneously so it will get hot. I usually use the first option (which tests your CPU a lot and heats it up the most). If it doesn't overheat like this, it won't when you're gaming. Run it for about half an hour, that's really all it takes.