Thanks again for the reply bu99zy! I appreaciate your help...
I actually opened a bug in the KDE bug tracker after posting this (bug 301022), and the fine folks in the KDE community helped fix the problem. Thankfully, I got my desktop working without having to uninstall any of my plasmoids. (It's still good to know where they're stored and how to remove them though, so thanks for sharing that
It turned out to be a settings issue: my .kde/share/config/plasma-desktop-appletsrc config file got corrupted somehow, and the desktop's depth value got changed such that it was being displayed on top of everything else. Because of this, windows and panels were hidden behind my desktop. This also explains why the windows became visible when I killed the plasma-desktop process.
I replaced the above mentioned configuration file with that of a brand new user. This fixed the problem by reverting all of my settings.
I still don't know why my configuration file got corrupted, and why this seems to happen to me regularly with every KDE distro I try, but I'm really glad that I got my plasma desktop working again. The only downside, is that because I can't understand the contents of plasma-desktop-appletsrc, I couldn't selectively modify it to fix the problem, and in replacing it altogether, I lost all of the customizations I made to my desktop (to the panels and such). Either way, I'm extatic that I've got my KDE working, and I don't have to switch back to gnome