So, I figured out what the problem was. Without getting into too much technical detail, let's just say that I learned a valuable lesson about dereferencing. Yay!
Doing this Jotto project has really helped me learn Perl. No amount of exercises in books would have taught me as much or held my interest as long. I am very happy programming games for now, and maybe I'll move onto other things later. But, for now, I'm learning plenty just playing around. Who knows what else I'll end up learning working on this and other game projects. Did I have any clue that I would need to learn about multidimensional arrays and references in order to work on this project? Nope.
Every day an adventure.
Time to get off the computer now, before my shoulders start hurting even more.