But the book would be more about the consequences of this - do they eventually take the thing apart and jump-start a silicon chip revolution in the 1950s, or (more likely I think) does the government destroy the machine as the UK government did to the Bletchley machines after WWII, and because there's no ground-up computer theory does it set back computing for decades?
So now ask somebody really smart in that technology, like say Jay Forrester who had just finished inventing core memory, to analyze this magic beige plastic box. He could probably recognize that the PCB provided connectivity between parts, but what are the parts, these little flat plastic tiles? I don't think it would be possible to work out from first principles what the functional contents of a DRAM chip is, let alone the CPU. Even if they x-rayed it, supposing they had x-ray tech with enough resolution to resolve a chip, how could they figure out that those little blobs are transistors? Transistors hadn't been invented!
I think they'd have to concede this is "sufficiently advanced" tech, in Arthur Clarke's phrase, to be indistinguishable from magic.
The RAMs and ROMs would be fairly trivial to figure out, as well.
You might not learn the manufacturing process -- that really did take a couple decades of material science and physics advances. But the principles of the machine would be clear. And then you could take the knowledge of that and scale it to the electronics components available in the era. You'd definitely have a head start simply knowing that these things were _possible_, and getting a boost on knowing how a computer could be structured.
Given that knowledge they can try breaking those pieces of plastic apart to see that it's a housing over some sort of ceramic core. Using spectroscopy and chemistry you can figure out what that core is made out of. Now you know what mix of chemicals allows for really high density data storage and computation.
Using x-rays and microscopes they can figure out that the little ceramic die has some sort of structure etched on it. Maybe remove tiny pieces to see what different parts/layers are chemically composed of.
Now they know that there's something interesting about certain elements deposited on top of silicon using some sort of etching approach. Early transistor research was already well along (and had been patented already in the 20s) so it's likely they would have made the connection. Given all that you can start brute forcing industries and ideas around those materials.
You can see both copyright dates, and plenty of other English text. While in 1940 this would have represented incredible futuristic technology, it's pretty obviously made by humans and not a piece of alien magic. It also has components like resistors and capacitors with markings which would have been immediately obvious to 1940s electronics experts.
From Greer's point of view, the factors that make today's hardware brittle are not technical, but economic. Corporations have to make electronics at a profit, and at a price point that is accesible to the average working class citizen. This business model would not be sustainable in the either a fast-collapse or slow-collapse scenario.
Instead, in the novel, governments take over the tech industry sometime in the second half of the 21st century, and treat it as a strategic resource in its struggle to not be left out in the global musical chairs game of climate change + resource depletion. They run it at a loss, and put the best minds they can spare to the task of making a computing infrastructure that is built to last.
By the 25th century, which is the time when the novel's events take place, Humanity has lost the ability to manufacture electronics, but computers built 350 years ago are kept in working order by a cadre of highly trained specialists (most of which have the skills of a geeksquad employee, but still). Common people have maybe heard some wildly innacurate legend about robots or computers. Wealty individuals are probably better informed but still cannot own one of those at any price. They only computers depicted of spoken about are US government property operated at US millitary facilities (or maybe there was one at the Library of Congress, do not really recall, though).
There's one post-collapse hacker in the novel, a secondary character that is part of the protagonist's crew. The author is not an engineering type and dances around the actual skills of this guy, but I'd say he seems able to use a debugger/hex editor and read binaries. His greatest achievement, though, is to fix and set up an ancient printer and recover documents from a disk that was "erased" but not wiped clean.