Very random BSOD and rebooting, new HP computer

Hey, I got a problem with my HP Dv6 laptop. It reboots or gets BSOD very frequent and randomly. When I play games, when I download (especially using torrent), when I browse demanding internet-pages, when I install things... It feels as though it gets problematic when the CPU (alternatively GPU) is running hard, but in some cases that can't be the problem. Also, sometimes it doesn't BSOD, not even under heavy pressure.

I have a feeling this might be some serious and that I should send it back at HP, even though no tests (disk test, memory test) has shown any problems.
But I thought someone here could take a look at it in case it's a silly driver problem or something with the settings. I need the computer for school-work, so I don't want to return it unless it's necessary.

Oh, and my computer is Norwegian, so some of the attached info will be in Norwegian. I guess file names, error codes and the most important stuff will be in english, so I hope someone still can make something out of it:)

My windows 7 is x64, home premium, original OEM.
The system is a few months old, same with the OS.

So, should I add some more information? Some help would be greatly appreciated:) I guess I can add that I get about 4 different blue screens.
I also noticed that the system health report found 3 or 4 problematic files, all somehow related to networking, I think. So I tried to update some network drivers, but with no luck.