Audio in to Audio Out

No, it's a hardware issue. The circuit is designed for input so software can't touch this, unless there's something weird going on. If you need two outputs, any reason you can't use a 3.5 splitter?

"The Wikipedia page for your dell shows it has HDMI output.
If your default audio is diverted to that path you might need to do some changes with your mixer settings for getting the audio back to the audio-jack
(I presume you have one, did not see it listed on that wikipedia page;
Meanwhile this Dell page says there is one audio-out jack, does not mention HDMI).

Then you need to identify how your speaker connectors work -- do you have a 3.5mm stereo pin?"