Go to Start -> Search -> c:\windows\minidump to see if your computer has blue screen'd and automatically restarted. Typically, your settings should allow a crash to output what is called a dump file. This is a memory dump created by Windows as it detects that it is no longer capable of functioning, usually due to a hardware, serious software conflict, or memory error.
If this area is blank, and the issue never pops up again, considering letting a few days ago by. If this is a new set up, you are still under warranty. You may want to test the integrity of your hardware using what are known as burn-in utilities. Many of these utilities are free, used in IT pro environments extensively, and will help determine if your CPU/GPU/RAM and hard drive components can handle stress.
Some great samples of this freeware:
prime95 (burn-in CPU and memory stressing)
memtest86+ (CD/DVD/USB for booting into a thorough RAM scanning test)
For graphics cards, many benchmarking tools are out there for commercial use, which are also used for stress testing. One of the best ways to really test your graphics card to the limit, is to, literally, run a program or more likely, play a highly intensive game for a prolonged period of time. This is the cheapest way. If your system suddenly crashes and you get a blue screen listing suspect files from AMD or NVIDIA, you will have a good idea something is wrong, especially if it happens consistently.
Unfortunately, you're going to see what I'm talking about with PassMark right here:
PassMark BurnInTest software - PC Reliability and Load Testing
It costs money. We have no affiliation or coupons to give you for this one. If you want to try something different, run your GPU with a high powered game. If the system consistently freezes, we can even analyze minidumps for you. But its probably the root cause.
If your system goes dead for no reason at all on the desktop with nothing running, it could be any manner of issue, and that is why you should run prime95, memtest, etc.
Before doing this all, go to Start -> Run -> Event Viewer
Start -> Run -> View reliability
Look at these areas to see what could be wrong. There is no silver bullet for these problems until you, yourself, collect additional information. If the build is not working for you, it could be any number of issues, but if you get to the point that you've been driven mad by the errors, be aware of warranty and RMA time. If you find a faulty component, you may need to work fast to have it replaced.