I've seen similar issues on the forum, I've tried uninstalling the Realtek Audio Device from the Device Manager (ticking the uninstall software option also), and reinstalling them.
I've tried audio drivers from Realtek and also the drivers Windows installs after rebooting. I've also tried the drivers from this Dell FTP: http://ftp.dell.com/Browse_For_Drivers/Laptops/XPS/XPS%2014Z%20(L412z)/#Audio (the one listed under Audio - Driver).
In all cases, the audio out through speakers is fine, and when I connect headphones (tried many) to the headphone jack, I get the notification "You just plugged a device into the audio jack" from the Dell Audio software, and under "Jack Information" in that software I see it shows a headphone is connected, and the audio stops playing from the laptop speakers as expected (suggesting the jack connector and internal wiring etc are OK)
I can see the audio levels look OK in Windows Mixer, but no sound from the headphones at all. I also tried disabling the device in Device Manager, rebooting, then re-enabling but no luck.
I later installed Ubuntu (dual booting), and the audio plays fine through the headphones in Ubuntu, so it seems like a Windows drivers issue.