I am not an expert at this, so you can see what others say too. My opinion, if you replace a "bad" box with a "good" box and the problems go away, that would seem to eliminate problems in your electrical circuit as a cause of shutdowns.
Based on things I have read in this forum and limited personal experience, I would be suspecting bad power supplies (or other bad components affecting the power supplies)as the cause of your problem, which is why I suggested talking with Dell if the boxes are still under warranty.