HTML::Parser is not core module, and it is (was) installed on the server. After Perl update it can't be found anymore by the perl. And I believe that if you update Perl installed modules remain - simply because it would be stupid to be other way and require from you to install all the (non core) modules after each Perl update.

I suspect that the sysadmin (who I assume did the update) didn't do the update right - and somehow forgot to include the folders where non-core modules are installed in the INC.

I've been trying to figure out how to add stuff to the @INC for the whole server - Config.pm seems to hold some of that info on Windows, but I'm not sure for FreeBSD (probably the same). Also not sure about where it is specified where to look for Config.pm ...