OK, today I tried to get XML::LibXML working.
Again, I failed because a necessary DLL wasn't installed: this time, it was libxml2.dll.
Thanks to the power of Google, I found "Installing an XSLT processor" fairly quickly. This linked to Igor Zlatkovic's website, which has since moved (the correct page is now http://www.zlatkovic.com/projects/libxml/index.html).
This page contains Windows binaries of libxml, libxslt, libexslt, and iconv. Let's see how far I get with those.
Edit: Hm, no dice: doing
perl -MXML::LibXML -de1 complains about not being able to find
xmlIndentTreeOutput in libxml2.dll. Darn.
Edit 2: I finally found a suitable libxml2.dll—at any rate, I can run
perl -MXML::LibXML -de1 without any pop-up error messages. I got it from http://theoryx5.uwinnipeg.ca/ppmpackages/scripts/.
Edit 3: There's a small account of my searches in an email to the Perl-XML mailing list.