TL;DR

Let's say that computers were invented at a school for the blind in mid-1800s. How would today's technology, based on these non-screen-based computers, be different?

ETA: To clarify and hopefully narrow this enough -- I'm assuming that both the newer products will be influenced by functional computers predating movies & television: radio & telegraph/telephone may be more of the communication models. Also, that just like numpads on phones and computer keyboards are arranged differently due to vestigial bits from their separate origins, and our "Save" icon may confuse those who hadn't grown up with 3.5" floppies (I'm from the 5.25" era myself - Apple //c!), and we still call that thing in a car a "glove compartment" despite not wearing specific driving clothing any more).

So while sighted potential users greatly outnumber the blind ones, they're from a world where computers have always been fully accessible to the blind (so accessibility is not an afterthought), and that has probably driven the development of the CS field for quite a while.

Background elements

Braille had already been invented by the early 19th century, and it was derived from a military application (Night Writing, for Napolean's army) -- much like our computers (stored programs, some of the more theoretical elements were codified during WWII ) https://en.wikipedia.org/wiki/Braille

Punch Cards for Weaving had been invented in 1803 -- for a while schools for the blind were often trade schools-- the first one (https://en.wikipedia.org/wiki/Institut_National_des_Jeunes_Aveugles (first school for the blind was also named "National Institute of the working blinds", and was famous for graduating Organists.)

So now let's say they got an early Jacquard Loom head type machine (instead of Organs)
from https://en.wikipedia.org/wiki/Jacquard_loom#Importance_in_computing

... The ability to change the pattern of the loom's weave by simply changing cards was an important conceptual precursor to the development of computer programming and data entry. Charles Babbage knew of Jacquard looms and planned to use cards to store programs in his Analytical Engine. In the late 19th century, Herman Hollerith took the idea of using punched cards to store information a step further when he created a punched card tabulating machine which he used to input data for the 1890 U.S. Census.

(Note that this Loom appears to also be a French invention.)

Charles Babbage & Analytical Engine - according to Wikipedia (sorry that I keep going back to that source, but I'm assembling fragments of things I thought I knew or picked up (I'm no tech historian), and Wikipedia's the easiest place to assemble the threads.) -- he was self-taught from reading many mathematicians, some of which were French, and was definitely fighting the British Establishment.

from https://en.wikipedia.org/wiki/Charles_Babbage#Computing_pioneer

While Babbage's machines were mechanical and unwieldy, their basic architecture was similar to a modern computer. The data and program memory were separated, operation was instruction-based, the control unit could make conditional jumps, and the machine had a separate I/O unit

So a computer doesn't need to be print-derivative

We have punched cards (tangible, non-alphabetic) manipulating rules and representations of numbers. As Ada Lovelace said:

"We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves."

So what if punched cards went in, braille results came out? Things may have stayed mechanical longer, instead of moving to processors as we know them, but there'd also be almost a century's extra progress. "Screens" may have moved to Refreshable Braille Displays - but would there be "windows" and other simultaneous processing?

The "World Building" or AltHistory part --

Just like the Internet was very US-focused in the beginning, so it has some legacy effects on domain names and rules, perhaps in this world, the computer world (and thus internet?) were dominated by French research, and blind computer scientists. Look at the Minitel for an example of France being way ahead of the curve! They started as phone-book replacements, but provided message boards and finance stuff.

why I'm asking

I'm documenting navigation of applications designed with minimal concern for accessibility. My particular job seems to be describing how to navigate web applications for screen readers. Screen Readers (which read aloud text to blind/low-vision computer users) address everything in a pretty linear way. (Also, we have to keep all navigation keyboard-focused -- it's more predictable than a mouse.)

When windows pop-up, where did the focus go? Do the users know there's a new dialog on screen? Where does the focus go when the error message goes away? (To the last place it was, to the line with the error, or to the top of the page?) It's easy for the sighted to notice a missing field, the blinking cursor, or that something changed on the screen: but if the default were audible and tactile? How would the interfaces change?

What different communication elements may be emphasized? Would casual computers (like cell phones) do the same things or different ones?

I know answers could go in a steam-punk way, but they doesn't have to, or the proposed tech doesn't need to stay that way.

Youngsters. The first computers read and wrote punched cards or punched paper tape; they did not have any kind of user interface where being blind or sighted mattered.

It was perceived as major revolution when some smart technician adapted a typewriter to be able to print computer output; electric teletypewriters were then adapted so that operators could type commands into the computer. But teletypewriters are still purely linear devices.

Up until the late 1960s or early 1970s most users did not even see the computer or come anywhere near it. One wrote a program on a special form, the nice ladies in the card punch room converted it to punched cards, the cards were given to an operator through a wicket, and a note was made in a register; one day later one queued to receive the cards back, together with whatever output the program had produced, printed on 132-column fan-folded paper.

(Ever wondered why terminal emulators have options for 80 or 132 characters per line? That's why. A punch card could hold 80 characters, and was assimilated to one line of input. One line of computer printout had 132 characters. Those numbers were burned in the collective memory of informaticians.)

Up to this day operating systems in the Unix lineage are ready to interact with the user via a dumb terminal, with no graphics and no full-screen character cell capabilities.

The conclusion is that it doesn't matter where the first computers were made. It doesn't matter whether the inventor and the first users were blind or sighted. The first computer terminals which had the ability to run full-screen cursor-addressable character-cell interfaces (not graphics, just a rectangular array of characters) became available in the mid-1970s; that is, a staggering 25 years after the introduction of the UNIVAC I, the first commercially available programmable computer, and 30 years after the first well-known programmable computer, ENIAC, became operational in production for the U.S. Army. A full human generation separates the first computers from the first user interfaces where being sighted was necessarily an advantage.

I see no differences in how computer would have developed.

The first computers used punched cards to take input and give output (one of the favorite prank among nerds in those days was to swap two random cards in the physical folder containing them, when the owner was not paying attention), and graphics came much later.

And the reason is that when you move to mass usage, you have to rely on something fitting the masses. Punch cards aren't. Braille isn't, except for those who have to learn it. But we as species use sight as main mean of communication, so it is inevitable the usage of graphics.

I think the biggest difference would be in the development of user interfaces.

If computers had been designed primarily by and for blind users, I imagine a much more sophisticated version of the Refreshable Braille Display would be in common use by now. I'm imagining a grid of keys instead of a single row forming a kind of tactile screen. This would allow for parallel processes happening in different zones on the grid, like windows. Users could tap in a particular zone to get an audio readout of that process, to advance the readout, or to drop the cursor and start typing; much like modern haptic screens, different touches could indicate different actions. An audio cue could alert users of a pop-up alert, which would always appear in a designated zone. Afterwards, the user could return their hands to whatever process they wanted. Audio cues could also alert users to things like empty fields; if the grid is labeled like a battleship board, then an alert like "Input required in Zone M6" could be used to direct the user.

If blind people continued to be the primary developers of computers past the initial stages, advances in tactile interfaces would probably have replaced the advances in graphics. A tactile screen, like the one described above, would be a mechanical marvel, but wouldn't require much processing power to run; certainly nothing like playing a video. So the push for more and more powerful processors wouldn't have been as great. The tactile screen might be able to produce static images, by pushing pins up to form the outline of a shape, but probably most entertainment on computers would be in audio form. The podcast boom would have come much sooner, probably replacing the YouTube boom.

I hope that helps!

I think a good technology to consider in comparison is the telegraph. The telegraph also began as a technology processing bits of information that while accessible, in that they used the sound/touch of tapping, was also cumbersome to use in that it required the user to learn a specialized code to both input and interpret. So, you had a specialized profession develop around the telegraph, which gave way when an interface easier for the layman (the telephone) was developed. So, if you have the adoption of punch card computers a good century before Cathode Ray Tubes were sophisticated enough to create purely visual displays, you need to think about how you would stop CRTs from overwhelming punch cards and Refreshable Braille Displays.

Keeping telegraphs in mind, one interesting possibility is if your early punch card computers could interface directly with telegraph lines. The French were already pioneers at long distance communication: under Napoleon, signal towers were built connecting Paris to the frontiers of the country. What if a series of punch cards at a central computer in Paris could be sent to a punch card writer in Marseilles almost instantly? You could have a sort of internet under Napoleon III!

Ultimately, though, I think tactile interfaces are going to be hard to catch on very widely, even with these boosts. The best bet is to try to stimulate a jump to more audio displays. This is where a lot of technology is trying to move now: a natural language interface, like Siri or Alexa. Maybe if a punch card internet develops, you'd still have specialized data entry types for input, but the displays would instead become temporary phonographs?

Honestly, there are a lot of repercussions that could come from this, but good luck exploring! Some other resources to look at are 'Jacquard's Web' by James Essinger, a non-fiction book on the development of the Jacquard loom and some of its significance, and 'The Difference Engine' by William Gibson, which not only launched the steampunk genre but also deals with Babbage-style central computers as the major point of departure for the world.