In the end I answered this, contrary to all the other answers, that it might be possible.
"The greatest challenge absent survival seem to be to meet the conditions for some decent metallurgy, but if this is managed, and all the mining and transport doesn't need to be a problem if there are carefully selected semi uebermenschen involved, the next step is to generate electricity using the metals. Id say in 50 years they can have built a basic circuit and from there on it is just few more steps to a computer, though not a very useful one, as a display involves a lot more comprehensive industry than a crude processor."
So now Ive spent quite some time wondering if Im right.
It all depends on acquiring the minerals.
" The strong do what they can do and the weak accept what they have to accept. "