when you turn it on, immediatly after the bios hit F8. it will give you advanced boot options. one will be disable automatic restart (or something similiar). this will allow you to see what the BSOD is, and help narrow it down.
also, it may have diagnostic software (the bios splash screen should mention it) that will give you an error code if it is hardware based. i mention this because a dell laptop at work did this and his Harddrive had failed.