Based on what you posted, the first thing that comes to my mind would be RAM. Hard drive light makes me think the memory is dumping. Speed is directly related to RAM. (in most cases)
Swap the ram chips and see if the problem follows to the other computer. Quick, free and easy to check...
How long does it run before it craters?
The good thing is you have two identical machines. You can swap components one at a time and isolate any hardware problem.
If you swap the hardware and the symptoms remain, reload the OS.