I've actually got the exact same sound card (Dell E1705) and I've got a slightly different problem.
Just to verify, my lspci output is the following:
00:1b.0 Audio device: Intel Corporation 82801G (ICH7 Family) High Definition Audio Controller (rev 01),
which seems to be exactly the same as yours.
My problem is this that I can't get Audacity 1.2.6 to recognize my sound card for playback, although I am able to choose it for recording. However, when I try to record, it doesn't pick up anything, even when I've got music playing in the background. I'm using the ALSA drivers (which I assume you are too) and I realize that Audacity claims to not be compatible with ALSA without compiling with a special option (PortAudio v19), so I compiled the current beta version to use this newer version. I still can't get it to recognize my card for playback, but I can get it to (try to) use it for recording. But on the beta version, it doesn't even try to record (the red indicator just stays at 0 and spazzes out until I hituse stop).
Are there any special options that you're using for Audacity or your ALSA drivers that may help me out? Strangely, I'm not able to get it working in Virtualbox either (which I'm not too surprised or worried about), but booting into Windows XP Pro deals with it just fine.
Thanks for your help in advance!