Headphone jack not recognizing speakers or headphones on Inspiron n4110

Hi there,

I've got an Inspiron n4110.  When I plug speakers or headphones into the speaker jack on the side, the computer doesn't recognize that anything is plugged in.  It simply continues playing out of the built-in Dell speakers on the front of the machine.  When I go into Control Panel > Sound > Playback, I see that the only audio playback devices the computer recognizes is the build-in speakers on the front ("Realtek High Definition Audio").

What's the deal?  How can I play sound out of my speaker jack into my speakers/headphones?