MacBook Pro 2016 (sans touchbar) – headphone jack not going all the way in

It's likely that the controller for the trackpad and keyboard (I believe it's one chip for both) is dead. I had an issue where the keyboard and trackpad on an older pre-unibody model would become non-responsive, but the rest of the top case components were fine (power button, back light). It was tracked to a faulty controller in the top case, but the solution was to replace the whole thing.

iFixit sells replacement top cases, but they're rather pricey ($299.95 for the A1260-compatible part). You might be able to find a cheaper one used on Ebay or elsewhere. The repair itself is fairly straightforward.

Have you tried plugging in a USB mouse or keyboard yet? If the problem is what I think it is, that should work fine.

The red light in your audio out jack indicates that it is active. That is why you do not hear anything on the speakers.

Your analog/digital switch in the port is stuck -- the red light is the digital audio signal.

Try to plug the headphone in, this time wiggling it from side to side while it's plugged in.

Alternatively try cleaning the audio plug:

Try inserting a cocktail stirrer or a toothpick and jiggle it around in the audio output port and the internal speakers should come to life.

If you have a compressed air can use it. that seems to work best.

There is a switch inside that has to be tripped.