I just changed the configuration of my Web server when I encountered the problem in the title. Obviously, when I recompiled the server from the source optained from http://www.apache.org/ and http://www.apache-ssl.org/, I somehow managed to make it "forget" the LoadModule command. But how?
A quick search on the Web turned up a few dozen documents, but they were either questions posted to mailing lists or newsgroups without answers, or answers that were meaningless. Finally, I found the answer at the Web site of Halcyon Software.
The problem, it turns out, is that prior to recompiling the Apache server, you need to use the --enable-module=so option when running the configuration script for the Apache source. So to recompile the Apache server, you need to do the following:
cd /usr/src/apache ./configure --prefix=/var/lib/apache --enable-module=so make clean make install
Needless to say, you may require additional options when running configure, options that match your operating system and desired server configuration settings. On some systems, it may also be necessary to add --enable-rule=SHARED_CORE.