First thing is to tell us the name of the equipment manufacturer.

Second thing - given the variety of semiconductor manufacturers (westinghouse, Motorola, AMD, TI) is there a possibility that these could be MIL type numbers, rather than a manufacturer's internal "catalogue number"?

Since all chips are labeled with at least the manufacturer's logo (Ti, AMD, Motorola, etc.), you could try asking them if they still know what these chips are. There are also old books that lists all these chips and their replacement parts.

Are any of these parts are actually broken?

Context means everything. Sometimes you can see kinda what the components are doing, maybe find data sheets or cross-references for some of the original parts, and replace them with close-enough alternates. If you're not experienced with reverse-engineering electronics, then it may have to be a team effort. But, luckily, there are communities of people interested in getting particularly uncommon bits of hardware up and running again.

The individual components are numbered for the vendor, where you see 930xxx or TR-xx. This is how a lot of General Electric designs are labeled, among other vendors who follow/followed the same design style back then. I see it every day at work with the old electronics and computer equipment I maintain. The components without the prefixes are likely replacements. You'll need the schematics/BOM for each board or the overall piece of equipment.

So in your first picture, those are transistor arrays since you see the one has been replaced with an RCA CA3081. It has been replaced outside of vendor support since it doesn't have the proprietary part number, after the warranty expired.

For any of these, you will likely have to go back and trace several generations of equivalent replacements.

Thanks guys, too much work for too little pay. I replaced every single capacitor and it still blows the fuse on the computer panel and that is full of these unobtainable parts. The tube appears to be working but that's as far as I go for now and I don't have nearly enough knowledge to do anything more without risking further damage.
It's that Bunker Ramo 2200 terminal BTW so I don't even know what I'm supposed to be seeing when it's working properly. Zero support for it online.