I recently picked up this computer used. It's an older model, but it still works good. I am primarily using it for the kids to watch videos.
However, recently, the sound from the external speakers stopped working. I had done all the Windows and Dell updates about a week before, and had it disconnected from the Internet.
I've updated the drivers, and the system detects the speakers and acts like it's playing audio. But no sound from the speakers. I've verified that the speakers do in fact work on another computer. There is no warning symbols in Device Manager, and everything is up to date. The built in speakers work, just not the external ones, which leads me to believe that it has something to do with the audio jacks.
I would try running system Diags here by entering your Service Tag just to see what happens, and next when you plug in the external audio see if it is being recognized by the system (like do the internal ones stop working?). If the internal ones stop working then that means there might be another setting we're missing, but if they continue to work and the system doesn't even acknowledge the external speakers then I think you might be right on this being an issue with the jack.
If it is an issue with the jack, an option might be looking into buying a USB to audio converter which should be a quicker fix that replacing internal hardware.
Let me know if you have any luck on the diags or troubleshooting steps.