If you were using Firefox Sync and were actually signed in to your browser, you can get back all those favorites by signing back into your Firefox account on your newly repaired computer.

By the way, your use of the word "Favorites" instead of "Bookmarks" makes me wonder if you were actually using the Firefox browser at all. That would make a great deal of difference to your attempt at following this advice.

Data can be recovered from a 'damaged' hard drive. It depends on the real damage.

An electronic repair shop could answer that question.

As I stated in my original post, I'm a novice. I obviously don't know enough about computers to tell you guys what you need to know to give me a useful answer, so I'll return to the tech that replaced my hard drive and see what he can do. But thanks.

I have a similar problem, in that I replaced the hard drive on my wife's Mac with an SSD. Everything is backed up to Time Machine. But sync doesn't work, even though she's signed into her account.

Same problem here on Windows. I upgraded to an SSD. I still have my old hard drive. Firefox sync doesn't work when I log in. Can't find bookmarks and history. Profiles contain nothing too.