So apt-get told me I had a broken package, and recommended that I run apt-get with some parameters to clean things up. It said it would remove a bunch of packages, and the list looked okay to remove to me, mostly stuff that I didn't use anyway or I didn't know what was. Apparently, something in that list was essential, since Gnome disappeared. Hmm. A reboot left me at a command prompt. So I did "startx" and prayed, and did indeed at least get X to start.
I'd been wanting to try out Openbox anyway, so this seemed like a good time to do it. It turns out Openbox is probably the window manager I'd been looking for when I dumped KDE for Gnome. It is easy to install:
sudo apt-get install openbox
Add a line to your ~/.xinitrc file:
Then "startx" will start Openbox. Openbox is perhaps the most configurable window manager I've ever used. The downside is all the configuration is done by editing xml files by hand. For example, to get Open box to rotate from desktop 1 to 2 to 3 to 4 and back to 1, it was a simple matter of editing my ~/.config/openbox/rc.xml file to change <wrap>no</wrap> to <wrap>yes</wrap>, which was way easier than the scripts necessary to get Gnome to do the same thing.
There are a few things I'm missing that I haven't set up yet, but for the most part, I'm liking Openbox a lot.