Your long reply, I thought, very helpful.
BTW, back in the days of the C64, I had a friend who had one. Laugh, of course, I had an Atari 800, but if you don't hold that against me, I won't hold the C64 against you.
If you have 40+ years of IT, even if working "with" IT folk, you likely have a lot more general knowledge, then you might realize.
Regarding Cisco GUI capabilities, for "Enterprise" equipment, I think they have some support for it, by generally "Enterprise" network folk work with the CLI. (Cisco's SMB routers and switches, though, most folk might use their GUI interfaces.)
CLI access on Enterprise network devices, in the past was normally done via Telnet, but in the last decade or so, many have migrated to SSH. Basically, the same CLI interaction, just the interactive stream is encrypted. Of course, there are some other differences, but more with setting the Cisco device up to use SSH, and using a SSH client. (In some ways, conceptionally much like most Internet web sites no longer use HTTP, but now use HTTPS, but as a user, no real difference to the web page presentation.)
There are also various ways to determine logon on authentication on Cisco Enterprise network devices, from simple passwords configured on the device, to logons that require a RSA generate code, that changes "randomly" every few seconds, or users/passwords verified to external servers. (This is AAA in the Cisco parlance, and it has may various features.)
Often much access security is directed at across-the-wire-access, i.e. local "console" access often isn't set up to be as secure (assuming the network device is physically secured), but such "console" access can pretty much support what the across-the-wire-access can do too.
Traditionally, if there's a change of "admins" and you no longer have the credentials to access the device, Cisco Enterprise devices have a way, when you have physical access to the device, to "break" into the device. Newer devices, though, support a feature to disable that too. So, in theory, depending how security has been configured, if you don't have the admin credentials, you lose all access to the device. Possibly, if you return the device to Cisco, they might be able to pull the flash storage chips, and provide you a totally "clean slate", but don't hold me to that.
The reason I mention all the forgoing, depending on how an Enterprise device was configured, and depending on what information you have, you might not be able to configure it at all! This assuming you know IPs, and there's even more security wrinkles with those. For example, the device might only allow access to it, across-the-wire, using a specific device IP and/or interface and/or from a specific remote device IP. (In fact, the later might be called a jump box. You access one device, as another will only accept connections from that device.)
More than likely, your environment isn't doing any of the forgoing, but if it is, do you recognize what you're dealing with or what to do next?
Again, the forgoing is just issues with device access, let alone trying to figure out what was done, whether whatever that was done, needs "correction", and if correction is needed, what should it be.
With the IT background knowledge you probably do have, you likely have enough knowledge to start to better appreciate, the issues you might encounter.
I agree a great next step is mapping out your topology, what's were, and how is it connected. Knowing the IP to access a device can be useful (which might not be on a physical interface - often we use logical interfaces to host management IPs - something you would not "see" via CDP), and accessing configs; then understanding configs.
I believe, given enough time, you might suss this out, but it might take lots and lots of time. These forums, can help, in many ways, but if you have production issues, that you want to resolve, in days, or at most weeks, vs. months or possibly years, I still suggest you might need someone on hand to help you ramp up.
Once you've better documented the network (basically as it should have been, so you would already have this information), you'll likely be able to pare back such assistance, and better plan what you want to do next.
Back to my car analogy, it sounds like you don't have the factory maintenance manual, possibly not even the owner's manual, and possibly not even the right set, or full set, of keys.
Hopefully, the forgoing isn't too depressing, but then, personally, I'm a pessimist. But, the good side of that, I'm always being pleasantly surprised, rather than always being disappointed. ; )
