'There was a problem connecting to the server "…"' Alert Whenever I Open Excel

Of course, right after posting this question, I had an idea of what the problem might be and how to fix it. I figured I'd post it here, so that a future person might benefit from it, though:

Odds are, the problem was that, since I don't have that many Excel documents that I use on a regular basis, some document from that old server was still on the "recently opened" list. I couldn't get the Recently Opened dropdown menu to open (it caused Excel to freeze and the notification came up), so I just opened 10 different files, and that resolved it. Then, I did Command-Shift-O (because I realized that was another way to access the recent files list) and since that's a longer list, I found the files from that server and removed them from the list.

You could probably do Command-Shift-O and delete problem files from the start and avoid opening 10 excel sheets, but since that isn't exactly what I did, I can't say that with complete certainty.

My guess is that it was having troubles because these files on a server it couldn't access were still on the shortlist that shows up on the dropdown menu. It still seems like a design flaw to me that such an issue occurs at all, but until that flaw can be resolved, you now know how I solved the problem. Hopefully anybody else with the problem can solve it this way too!