I am also not to sure, if they (the remnants) would survive for long with global climate change and radioactive fallout everywhere.
If civilization were to collapse now, it may never rise again.
Also, there's plenty more available energy on this planet, many times the amount we've used so far in building this civilization. Methane Hydrate, Thorium to name a couple. We're just drunk on oil right now, but don't confuse that with 'using up all the energy.'
Dennis Meadows, of Limits to Growth fame, has noted that adding technology to his models does very little to shift the ultimate outcome.
And information absent energy isn't worth much at all. The world as a whole has effectively equal access to information. What's it's got unequal access to are raw material resources, most particularly energy.
And what do you mean, absent energy? There's plenty of energy around. Methane Hydrate reserves are estimated at 6X all the oil we ever found for instance.
We've also probably evened out the geographic availability (so for example you can scrape together a few hundred pounds of copper pretty much anywhere there is a little bit of settlement).
I agree that coal/energy would likely be a problem.
I wonder if the story itself is as fucked-up as my memory of it is.
This is because it confuses two very different things: ease of production of natural resources and cost effectiveness of production of natural resources. In the early stages of industrialization ease of production is paramount, but in later stages quality, production volume, and per unit cost is paramount. Early resources can be very much more expensive to produce and very much lower quality (as they were historically) and yet still be viable. Take coal for example. A small coal mine near the surface can be a quite viable source of coal in early industry, but such coal mines would not be economical in the modern era. Because modern coal is higher quality, much higher volume production, and mined out of areas where it is generally most amenable to industrialized production. There is an old abandoned coal mine within walking distance of me right now, I've been there and picked up coal off the surface of the ground. There's still literally tons of coal there that could be mined quite easily by hand. But compared to other sources of coal in the 21st century it's simply not economical to bother worrying about trying to extract it to depletion.
And the same exact principles apply to essentially every other natural resource. For example, we no longer mine bog iron because it's a very manual labor intensive work compared to, say, shoveling hematite sand into rail cars.
Additionally, this argument ignores the fact that vast amounts of resources will exist in the form of remnants of our present civilization (only the tiniest fraction of which will be vaporized by nuclear explosions). Huge amounts of iron, aluminum, glass, etc. will be left over, short-cutting the normal production process as for pre-industrial processes.
Re-industrialization after a collapse will be different than past industrialization but I see no indications that it will be very much more difficult and certainly not impossible.
Very likely we would return to subsistence farming. There would be little or no remaining industry, and not enough resources to support it. Generations would go by with little technological progress. Metal would rust away, buildings collapse, forests regrow, and after awhile there wouldn't be much left of our civilization. (This is of course assuming a worst case scenario where the whole world is bombed or a nuclear winter happens.)
When we did finally get around to trying to rebuild civilization, sure there would be some scattered resource deposits around the world, but not enough to do anything with. You can't build steam engines without perfecting metallurgy and abundance of cheap, strong, metal. You need to produce many tons of cheap coal, not just scattered surface deposits. The industrial revolution started when deep underground mining became possible by pumping out water, and those mines are exhausted or lost.
Some aspects of modern, industrialized civilization are tenuous (like worldwide inter-continental freight shipping), others are simply insights or knowledge gained through hard work that doesn't need to be repeated. Such as even the general idea of the movable type printing press, or literacy, or the germ theory of disease, or food preservation via canning, and so on. A modern person with a little bit of knowledge transported back 2 or even 3 thousand years could change the way people live their lives at a fundamental level. Boiling water and pasteurizing milk before drinking it are things that have been possible since antiquity. As would be canning of various foods, enabling preservation of fruits, vegetables, and meats harvested in the summer through the winter or through several years. That sort of thing transforms the basic subsistence equation enormously and massively accelerates the amount of time it would take to return to some degree of modernity and industrialization. Not to mention the huge transformation due merely to the ideas of rewarding individuals for their labor and their inventions, the idea of the scientific method, and the process of advancing knowledge and technology in general. All of which were stunted historically because people didn't know any better, just as people didn't know to wash their hands or boil their water.
Over the generations, more and more of the knowledge we've accumulated will be lost. The culture will change further and further from the one that led to our civilization.
It all depends, how the survivors will behave. I think it is much likely, that living together will change its form very much -- up to the possibility that people will fight for the last resources or a return to Middle Ages state (but, when I see what is happening in our democracies, they might also do without nuclear destruction).