Solution: Do not use a general apply drivers step (in SCCM) with the Latitude 3500. Another driver install corrupts the system. Driver cleaning might resolve in already deployed computers, but it's unknown which drivers are causing the issue since the obvious ones have been removed in previous troubleshooting. The most likely culprit for this bad driver is one that would be part of the driver pack for either the optiplex 9020 or 7040. I can't practically narrow it down further.
We have 270 of these, and ever since a feature update from 2 years ago, using a basic windows image and then loading both maxaudio and realtek drivers onto them, the audio jack is never detected when you plug another device in.  I do troubleshooting for many models of laptop and dell desktops, so I understand how the prompt and maxaudio works. But it doesn't on these. Updated firmware also.  I'm hoping a Dell rep or someone with latitude 3500s can chime in on how to make it detect when something is plugged into the jack. The odd behavior is that if you have something in the jack and restart the computer, it recognizes it as long as you don't unplug it. Not a good solution though.
Latitude 3500 audio jacks don't work.