It sounds as though your installation of Firefox is damaged. I suggest reinstalling Firefox 11 over your current installation to see whether that fixes the problem files.

Please make a backup first. See Backing up your information. (You can copy your entire Firefox profile folder somewhere outside of the Mozilla folder.)

You can re-download the Firefox installer from http://www.mozilla.org/firefox/ (green button)

Edit: One other thought, before reinstalling, you could try a clean profile. This will use your existing program files but none of your extensions or custom settings.

Close Firefox and start up in the Profile Manager as described in Managing profiles. Any time you want to switch profiles, close Firefox and return to this dialog.

Does that work any better (i.e., at all)?

Creating a new profile worked! At least, for most JS apps I've seen. JS-based ads on YouTube appear to work, as well as RSS feeds on the Lord of the Rings Wiki, but the main menu sliders on Gran Turismo Wiki don't work. Oh well, it's better than nothing. :D I'll probably try a clean reinstall soon, but for now at least I've got JavaScript working, for the most part, the way it's supposed to *knocks on wood*. If I do spring for a clean reinstall, I'll tell you how it works. Thanks!