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I built a "modern" version of something like this for middle school students.

https://github.com/mlyle/armtrainer

This is great! I think people think that kids need some cutesy or dumbed-down GUI environment to teach computer fundamentals, but this shows kids how computers really work at a low level.
Fun tangential fact. HP was then one of the main manufacturers of microprocessors. At the time (early 1980s) they had either in prototyping or manufacture at least three distinct lines of microprocessors; none of which they offered to the public, only for sale as part of a product.

The Nanoprocessor, [1] [2] which was a very fast and simple 8-bit microcontroller used in a variety of test equipment. The HP Focus, [3] a full 32-bit processor design used in their HP 9000 series. And the Capricorn, [4] a small BCD-oriented processor used in their calculators. By the mid-80s the first PA-RISC designs and HP Saturn would be out, too. Those were also only used inside HP devices, never sold directly for other users.

[1] https://www.righto.com/2020/09/inside-hp-nanoprocessor-high-...

[2] https://www.cpushack.com/2020/08/09/the-forgotten-ones-hp-na...

[3] https://en.wikipedia.org/wiki/HP_FOCUS

[4] https://en.wikipedia.org/wiki/Capricorn_(microprocessor)

The fab in Corvallis, OR, where a lot of the custom hp circuits were made later turned into a wafer fab for inkjet printheads. Still going on to this day although much smaller than before.
I still miss my HP 9000/715 (+735 at work), those PA-RISK CPUs and HP-UX were typical HP design excellence (and bleeding fast).
Remember having to write programs on this, or something very similar it while training in the US Navy in the early 90s. For most of the others in my class, it was the first thing they ever had to program - and we started with machine language (and ended there, too).
USAF Tech School, about 1984. Fantastic hands on labs. Also showed the use of the "current tracer", which was real cool. But I have never used one since. There was a wand that would sense current, and there was a device that you could touch to a PCB trace and it would inject a signal. With the current tracer, you could see the current disappear when it was shorted to ground by a bad PCB trace.
My grandfather, while a flight surgeon, learned about microprocessors on this beauty in I want to say 1983 or 1984. He later purchased one for us grandchildren and spent the 1980s and 1990s showing us how to program these devices. Most of us hated it but I fell in love - it definitely tracks that I was the only member of the third generation to go into tech (or at least directly).

Does anyone know of a firm that repairs these or a guide to fixing them one's self? Our's bit the dust a few years back and I have an inkling what's wrong but I don't want to accidentally make the situation more desperate by charging in blind.

Send it to Ben Heck, or any of the several other electronics YouTubers. Check interest/rate (if applicable) first, of course.

Good luck!

These are very simple computers. You could probably diagnose the problem with a multimeter and a logic probe (or oscilloscope). You'd check the supply voltages, then check the clock on the CPU, check the reset pin etc. But very often the problem is a capacitor that has gone bad, e.g. on the power supply.

Have a look at arcade game repair guides. This one seems decent: https://forums.arcade-museum.com/threads/how-to-fix-pcbs-a-b...

Make sure socketed ICs are properly seated.

Good luck!

I've checked the ICs in the past and there weren't any socketing issues but I haven't had a chance to take a deeper look at the board since then. I'll give it a more honest college try based on your encouragement.
The LED display driver is interesting in this device. It uses 75492 (still available!) for the digit driver and DS8871 for the segment driver. Except DS8871 is open collector, so it is used to force a segment off. For on, there 100 ohm pull ups. These are just the drivers, the latches are separate.

This is a circuit you want to optimize to reduce cost...

For comparison, here is a Z-80 "membership card". It uses 74LS145 for the decoder/digit driver (driven from a counter) and 74HC273 for latch+segment driver.

http://www.sunrise-ev.com/photos/z80/zmc-manual.pdf

The famous KIM-1 uses discrete transistors:

http://www.zimmers.net/anonftp/pub/cbm/schematics/kim-1/kim....

A really modern device might use an integrated LED driver, like TM1637 or TM1638:

https://www.amazon.com/dp/B01D140BT6/ref=sspa_dk_detail_0?ps...