Generally, if you are connected to the internet when you install Windows 7, it will find most of the device drivers and install them. The Dell specific sound driver is needed, as we have found (on the Dell forum) that non-Dell sound drivers either do not work or do not work correctly.
Make sure the SigmaTel is shown as the sound device in the Device Manager. If it shows something else, such as "HD Audio Codec" or "IDT HD Audio" that is incorrect. Also, if it shows more than one sound device (other than possibly a Video card audio that is used for HDMI), uninstall the other devices (Right click on an entry for the device and then LEFT click "Uninstall" and also check the box to uninstall the drivers), then restart the PC and you should be left with only the SigmaTel sound driver.
You can also check the recording devices in the Sound Panel. If the mic is disabled, enable that. If you are lucky you will also have "System Mixer" in the recording panel and set this for the default recording device (this allows recording streaming audio from the internet).