The first thing you always do in this situation, especially with a new PC, is to check to make sure all the drivers are up-to-date. Lots of times brand new PC's ship needing updates.
You need to do the above no matter what. But here's what I suggest you do if that doesn't fix it. If the computer is brand new and you don't have a ton of crap you are afraid to lose, just do a reinstall of Windows. You can try a repair first.
Other tools you can use to try to narrow down problems are the Event Viewer that comes with Windows, which will allow you to possibly see why you crashed. Then there's something like UserBenchmark, which can narrow down hardware problems if you know how to read the results.