Well, seems I was a bit premature in marking the thread as "solved". While I can access the internet with Firefox, it won't allow me to access sites like "Facebook". It states, "JavaScript Required". I checked "about:config", and found that JavaScript is enabled. So, I dunno what's up. It does work in Safe Mode, of course. Well, time to try the Refresh again.

Okay, I've refreshed it a couple of times over, and each time it goes and reinstalls all the old addons again, starting by going to this site here:
It's "Facebook Flash Video Player". And then all the addons are installed, and then, while I can connect to the internet, JavaScript supposedly is disabled (it's not disabled, actually).

Which addons do you have enabled?

Well, when in doubt, throw it out. So, I'm going to toss both /usr/local/firefox and /home/mark/.mozilla.

Have you tried removing all your extensions, with a fresh install of a barebones Firefox instance? I know you've been working with Safe Mode. The no Javascript error seems suspicious.

I suspect it was an old Flash Player install that was borking things. Regardless, I just got rid of Firefox Quantum and went back to Firefox ESR from the repositories. So, my bookmarks are gone and passwords are gone (I have records of passwords for sites I commonly use -- the rest was just clutter). I did remove the file /usr/lib/mozilla/plugins/libflashplayer.so. I'm not going to bother with a new Flash Player.

Stuff seems to be working okay now. It asked me to sign into the Firefox site (or Mozilla site, or whatever) where it promised that I could sync everything on all devices to what I had previously. I declined to do this. I just installed the uMatrix addon. I used to have NoScript as well, but I think uMatrix on its own will be fine.

Anyway, stuff is now working.

I definitely recommend a password manager. Not something that lives on a company server, like 1Password or Last Pass, but something in which you can keep passwords locally: pass

Awesome. Glad it worked out. Sometimes bleeding edge isn't the best route.

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Thanks. pass looks like a good program.

Yeah, for Debian it's best to stick with what's offered in the repositories.

I saw on Reddit that other people were having this issue with Firefox 67 too, and other people were not. I think it depended on what addons and plugins people had. Anything deemed unsafe resulted in being blocked from the internet (a rather extreme decision on their part, IMO). I'm not exactly sure what was going on in my case, though I did have a whack of addons and some unnecessary plugins. For me now, it's back to a just a couple of addons and the default "OpenH264 Video Codec provided by Cisco" which Mozilla itself installs.

I recommend https://keepass.info/ - you might want to have a look before deciding which one to use.

Cool. Feel free to reach out if you have any questions.

There are extensions that connect to pass for Firefox and Chrome.