With a Dell, the Dell sound drivers must be used. Non-Dell drivers will either not work or not work correctly.
Reinstall the listed chipset drivers and then the Dell sound driver (install the "Dell" sound driver, not the IDT listed as its an older driver - the "Dell" driver is an IDT driver too). Drivers and Downloads | Dell [United States]
If this does not fix it, the Dell Laptop audio or general hardware forum would be the best place to post, as there are those there familiar with your Dell. Laptop - Dell Community
I used to do a lot of user support on the Dell forums but it was primarily Desktops.