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Convince someone to pay you to write code. That can be a great motivator to learn.
If you're employed,
convince the boss to pay you to do projects using Perl.
If that fails,
identify activities where Perl could save you time and effort,
and do the work on your own time.
Join a Perl-based project at sourceforge.net (or other online repository): see the 'Project Help Wanted' section. Find a project that you want to learn, study its code, connect w/ the other team members, add some tests, fix bugs, add features.
Be a mentor to people looking for help (eg, answer questions at perlmonks). Teaching something is a good way to learn it.
Write an article about a topic you want to learn.
Learn to manage your own desktop machine effectively, so you don't have to rely on the IT help desk. Perl has many tools for sys admin tasks. See the books on Perl for sys admin (eg, Automating System Administration with Perl). Build your own custom toolbox that you can take with you to many different work sites.