I think this is an indication in and of itself: this is all I have concerning BOINC! When I trigger lsof, all I get about BOINC is what I copied. Which means, according to what you said, that the client doesn't open or doesn't exist. I searched my drive for other files (including both invisible and system files) and this is all I get:

BOINC [directory from Application Support]
BOINCManager [Application]
patterns-backup1.ini [all these are actually files from Firefox]
patterns-backup2.ini
patterns-backup3.ini
patterns-backup4.ini
patterns-backup5.ini
patterns.ini
recovery.js
upgrade.js-20161128075558
upgrade.js-20161129164126
upgrade.js-20161201172143
previous.js
recovery.js

I think at this point I have to admit defeat. BOINC on your machine doesn't seem to behave anything like it should and I don't know how to continue. Sorry.

Maybe someone with more hands-on experience on OSX can take over.

Please try running the following command in Terminal. You should see both BOINCManager and boinc in the list:

ps -axc

---

Charlie Fenton
BOINC / SETI@home Macintosh & Windows Programmer

Charlie, Juha,
Thanks a lot for your help, both of you. I found the problem and I feel a little dumb now that I've found it.
Throughout our conversations, I had kept wondering how that connection was not being made. I had ruled out macOS's Firewall and Little Snitch as the only rules I had towards BOINC were to allow all connections. It turns out that, in one of the old rules I had, 17 IPs were bundled up together and denied connection. One of them was 127.0.0.1. Though I am not sure of the intricacies of it (feel free to shed some light, it's always useful), I am assuming that this prevented BOINC's client from launching, since, as soon as the localhost was removed from the lot, the problem disappeared and the connection was made. I guess the fact that it was an indirect rule, bundled up with others, made it trickier to find.
Thank you so much for the time you took to help out, Juha in particular. I probably would not have persisted if it weren't for you. I am glad my computer will now be able to do its bit for the advancement of research.
Best,
D.