I know this is an old thread, but others may run into the same issue and find this thread in their search results when looking for answers.
To me this sounds like lack of PSU power, because drawing too much power from the PSU will make it unstable and hence make the system unstable, causing failure in memory, cpu, bus etc. and as this is happening randomly, it wont be the exact same way and at teh same point each and every time.
Be aware, that cpu power isnt as basic as so many watts, the total watts is just an expression of how much electrical energy it can deliver in total.
PSUs have 3 different voltage outputs (12v, 5v and 3.3v) from which you can draw only so many amps at a time.
So when it says for instance "700W" on a PSU, it means that those three circuits combined are good for delivering that amount of energy.
If you compare gaming oriented PSUs against office desktop PSUs even at the same total watt rating, you will typically find, that the watt ratings for those are very differently divided between the 12v, 5v and 3.3v part, where the gaming PSU will usually have more power on the 12v part and less on the other two, as the gaming computer will need much more power for the gfx board(s) which are 12v.