Have you also tried the swap technique with all the system parts
like trying a different RAM module
or try swappin the processor for another one and see if the same problems occurs, it could also be a motherboard failure
You said its not a software issue so it is obviously a hardware issue, but it could be any of the three hardwares malfuncitoning to cause the problem.
also are you connected to the internet?
if so have you got a firewall up and running and real time anti virus software running?
Because hakkers can attack your computer when left idle overnight, as mentioned in one of the issues of the pc advisor mag. and that could also be causing the pc to crash when left overnight running.