I read that story about 20 years ago, it was a French translation, so it may be even older. It was also a series, I'm quite sure that I read the first book of the series, but I never found the rest.

What I remember:

• The apocalypse in question was a world war, although I'm not sure if it was nuclear,
• Many devices/weapons left from this war are still working and affecting the world more or less randomly:
  • One device sends some sort of wave that render people unconscious for a time, the wave sweeping through the land at random,
  • Another device overloads anything based on electricity, effectively preventing the civilization that has rebuilt after the war to use such technology, despite having the knowledge and the means to build it,
  • Something is still active on the Moon and seems to be building some sort of screen in orbit that would hide the sun (this is part of the main plot, revealed towards the end of the book),
• The main protagonist is a female, head of some sort of scholar's order that is wildly known and very respected in this part of the world,
  • She is also a bit different from the rest of the humans: she's not affected by the 'unconsciousness wave' like the others, and her hair has some bird-like quality (thin and the inside is empty like a feather) and she finds someone else like her towards the end of the book,
• She tries to recreate a computer using people, giving them a very specific role (addition, multiplication, square root and so on) but her project quickly suffers from several drawbacks, including a manpower shortage,
• I think the story took place in Australia, but I'm not sure.