Before resorting to a reimage, I tried one final thing via ssh:
sudo dpkg-reconfigure -phigh -a
This turned out to be the last nail in the coffin of my poor computer. After rebooting, not only was all text replaced by little boxes on the login page (as had been the case before), but now there was not even a place to enter my password.
But actually at that point I was ready to reinstall the OS anyway. The fonts were not the only problem. As I had mentioned, Firefox and Thunderbird would not start. When I tried to reinstall Firefox via the Synaptic Package Manager, Synaptic seemed to hang. I eventually had to kill the process, again by ssh. It was then that I tried dpkg-reconfigure.
I reformatted the hard drives, reinstalled Ubuntu from a CD, copied back my data, and have by now reinstalled all of the important software I use. It took considerable time, but the computer is now up and running and back to normal.
I still have no idea what caused the problem; however, there is one recollection I might mention. When running "make check" on one of the software packages mentioned in my 07/24/10 message (I think it was cairo-1.8.10 but don't quite remember—might have been libglade-2.6.3 or pango-1.28.1), various graphics flashed over the desktop, overlaying items there (even after switching to a different workspace). So maybe it was a mistake to run "sudo make install." But it's hard to identify exactly what went wrong. I did a certain amount of tinkering along the way; for instance, when gtk+-2.20.1 wouldn't configure or make, after checking the log files and finding that it expected to find C header files from some of the other packages I've mentioned in strange places, I created the appropriate directories and added symbolic links to those header files. But regrettably I am unable to caution others as to the crucial stupid thing I did.
Thank you to everyone, particularly Laurens73, who offered suggestions or simply took the time to think about this thread. It is gracious of you to direct your energies to the ridiculous problems of a complete stranger.