Install the Maxx Waves audio software, that usually enables the system to detect the headphone upon insertion.  Since you mentioned it, the audio hardware in these machines is really bad.  The hardware requires bloated software to enable all other basic functions outside of "sound"  Perhaps that's why you're asking this...I'm sure this issue comes up a lot.
Headphone not detected when plugged in? What is your go-to fix? For more questions regarding this contest, please visit the Information Page here.
DS 07/21: Headphone not detected when plugged in? What is your go-to fix?