I used to do a lot of support on the Dell forum. There were some models that the system mixer was not incorporated into the drivers. Usually, Dell sound drivers are needed, but you may want to try a different driver just to see.
The Dell driver is an IDT 92HDxxx HD Audio and all the drivers I find doing a search just lead back to Dell.
You could uninstall the Dell and try the generic "HD Audio Codec" that Windows installs and see if that works.
Or try the generic IDT drivers IDT AUDIO Drivers Download
Before you do anything, set a System Restore point so you can fall back with System Restore if whatever you try doesn't work.