Does it behave this way with a different set of headphones?
No yellow/red flags
in Device Manager, especially the audio/sound?
No Problem Devices listed
in MSINFO32 (System Information in Win7) under the Component tab?
Carefully check settings in both the audio driver and Windows sound.
I would uninstall and then install
the latest audio driver. [or use
the Intel auto-updater to detect and provide the real
latest IDT audio driver. Note: It is possible Dell has disabled some of its bells and whistles in its driver version.]
It is possible that some wiring may be shorted not allowing the laptop to detect headphones being plugged in to disable the laptop's speakers.