OK then, we'll have to check some settings 
Click Start --> Right click Computer --> Properties --> Advanced System Settings --> Under "Startup and Recovery" click settings --> Under "Write Debugging Information", ensure Kernel Memory Dump is selected --> Ok --> OK --> Reboot your system.
Now, Windows should produce a dump when it next BSODs.
Since I don't have any dumps to go by atm, can you just do a very simple hardware test please? We might as well spend the time productively!
RAM - Please run Memtest86+ to check your RAM. A tutorial on how to do this is available here: Test RAM With Memtest86+ - Sysnative Forums
Regards,
Stephen