This may really be a hardware thing.
Hard Drives do not take much power. But they do require the power to be steady and free of noise. But the fact that it happens only when you are doing something intensive would suggest that is is not an issue with the drives and the PSU.
My best guess is that your CPU and FAN ware not working well together. The CPU overheats and the system goes down. Check you FAN. Bllow out the dust. While you are in there, blow the dust out of the PSU also.