I visited the apartment's admin office today, having prepared a little presentation about payment schedules and internet costs and whatnot, but all for naught: John from Daejeon was more right than he knew: the lady at the admin office stopped me short and said that, in all likelihood, internet service had indeed been provided by my previous company, not by the building. I told her that, when I'd moved in way back in 2015 (ten years ago!), I was able simply to plug in my computer and use the internet, so I had no idea which company was providing service. She said I'd need to contact my former company about that. I said okay, left to get lunch, and sent an email to my company asking what ISP they had used. Right now, I'm waiting for an answer (dinner plans got canceled, hence lunch).
The other thing to note is whether the previous ISP (internet service provider) was using its own company-specific hardware. If so, then I'm probably not free to get a completely different ISP. I think the big three companies in South Korea are SK Broadband, LG U+, and Olleh/KT. But it's no use guessing; I need to wait for my company's answer. Once I have it, I'll visit the appropriate office with the required paperwork (contact information, ID, proof of residence), and I'll see about getting a 6-month or year-long contract. If I bug out of the contract before the term is over (to move to Suwon, for example), there will likely be a penalty. Sigh. Unless it's possible to keep a contact while changing addresses (and paying extra for hardware installation at the new residence).
Another alternative is to forgo ISPs altogether and sign up for unlimited data on my cell phone, which can double as a WiFi hotspot. This would jack up my cell-phone costs by $15-30 a month (I'm on a 3GB plan right now), but from what I see on the SK Broadband website, basic "giga light" service is close to W23,000 a month, anyway. True, that comes to only $16 a month, but that also might be a promotional price just to lure me in. More research is necessary. So for the moment, all I can do is wait.
UPDATE (or as I pronounce it in my head, oop-DAHT-dey): My ex-company got back to me this evening and gave me the number for the internet guy in our apartment building (a service called Daecheong KT). It was a cell-phone number, so I wrote the guy a long text message explaining my situation and requesting a reactivation of service with automatic renewal. I also said that, if we needed to meet so I could present needed documents and/or sign anything, we could do that, too. I'm hoping to get service with automatic debit so I don't have to consciously remember to pay every month. Also, just to butter the guy up, I apologized for writing a long message so late. We'll see what happens tomorrow.