[https://www.youtube.com/watch?v=wZ_dfz_4bHA&t=21|This video] explains how to open the device (careful of the track wheel cable) and to push down on a certain piece to restore connectivity. Note: leave annotations on, as there are important notes to the effect of "do as I say, not as I do" to aid in your success.
This teardown can also provide a better view into the opening process: [guide|15366]
If that doesn't work:
In Step 3 of the teardown, you can see where the headphone jack is on the motherboard. I imagine you can get a new audio jack and switch it out. It will involve saughtering.
You got this!