In the 1700s, people started seriously experimenting with electricity, magnetism and general chemistry (as opposed to alchemy).
By the late 1800s we had thermionic valves and semiconductor rectifiers.
In 1949 we figured out how to combine semiconductors in order to make a "transfer resistor" (trans-istor). Followed rapidly by integrated circuits and avalanching into sophisticated nanometer circuitry.
There are still people alive who grew up on farms thinking that diodes and triodes were pretty neat new technogy and you can almost construct stuff like that using bear skins and stone knives. The hardest part, in fact, is the glass-blowing technology required, assuming you don't opt for some other similar vacuum-tight container.
A lot of modern civilization wouldn't be that hard to re-construct if we had the resources available. The knowledge is what took us so long to get here, and unless we lose all the knowledge and the knowledge about the knowledge, recovery wouldn't be a problem. What would hurt more is if we lost our transportation services. Most of what goes into modern electronics is not locally produced where I live.
So one of the most valuable professions might very well be landfill-miner, since the easiest way to get materials would be to extract them from what is now often buried as garbage.