Dell does not provide Windows 7 drivers for GX620 because they did not mark that desktop as Windows 7 compatible. But, you can get the Windows 7 drivers for the sound chip of the GX620 from Microsoft. I have tried all supposed compatible drivers.
I got it working by following the instructions from this website.
http://olabintan.com/2012/01/analog-devices-adi-198x-integrated-audio-driver-for-windows-7-on-dell-optiplex-gx620/