There has to be an uber suspension of belief as the game is a massive break from reality.
The big question is if there are parts, tyres and power sources how comes there are NO working cars or trains?
The reason for all the destruction is basically just the severe decay in human reasoning and spirit! There's enough resources, construction robots and plant to begin rebuilding! Why is everyone still living in corrugated shacks and makeshift buildings using cattle as transportation? You really have to leave common sense at home and live in the fantastical that this game is!
That said though I have been part of a few game discussion forums and many die hard fans look for a reality in them, it is actually normal for people to find any basis in fact in some of these things so my answer is of course hypothetical yet a possibility as to how it is supposed to work, ie my solution is that the terminals are located at the edge of the cylindrical hole much like that of an atomic bomb detonator works, the case is negatively charged and so too is the case of the core, it just needs a pickup point for the positive terminals