With a Dell, you need Dell supplied sound drivers. If you are not using Dell supplied sound drivers, that is the first step - install Dell drivers. I used to do a lot of support on the Dell users forums and non-Dell sound drivers usually do not work or work correctly.
HDMI generally takes priority over the sound card's output and usually the HDMI will set itself as the default audio playback device.
Dell does not support Win 7 on this model, but they do support Vista. Usually, Vista drivers work OK with Windows 7.
Here is the Dell Vista 32/64 bit sound driver: Drivers and Downloads | Dell [United States]