Broken headphone jack

IKf you are meaning the speakers don't work when the headphones are pkuged it, that's the way it's supposed to work. If you are meaning the after you plug in the headphones and then unplug them the speakers still don't work, that means you either have a dirty headphone jack or the jack itself is broken.

It is a definite pickup grounding issue causing hum/"buzz" which diminishes when touching strings. Check the impedance of cable jack inputs and cable which should be 1/4"mono input/output jacks) . A personal preference but effective is to NOT run guitar direct into mixer but through an external amp w/ a headphone out jack . Noise gating/preamp filter also will help eliminate the "buzz"/noise from pickups. It is unfortunately the nature of the "electro-magnetic" beast when it comes to electric guitar pickups .Hope this helps.

Does it change any when you rotate the plug a little?

You have to very, very, VERY carefully apply even pressure to both sides of the button when you pry it off, keeping it centered the whole time. Any significant movement off center will break the tactile switch it covers on the circuit board.

Did you check the solder connection on the jack where it connects to the motherboard? That's a high stress point and could simply be a broken contact that needs to be resoldered. Should be 3 or 4 pins likely.

Some keyboards use the amp output sockets for headphone use.
You might need some adapters for your headphones.
If it fell in, you would see an empty hole. This would be unlikely because it is held on by two screws. If all fails, buy an amp with a headphone jack input. Plug the keyboard into the amp and use the amps jack.

The probllem MAY be with the driver in the sound board. I would use one of your Aviom units right at the sound board interface and see if short direct connect works. I assume you power the A16D from the same receptacle as your sound board... IF NOT you are asking for damage due to ground bounce in your house wiring. You need a separate power run between your mixer an all other interconnected devices. The coupling from nearby lightning strikes could create enough electromagnetics to exceed the common mode capability of the devices. The drive from the interface at the sound board would be lower impedance and could easily be the most vulnerablle to transients as the protection is less since the drivers are assumed to be driving. If the power was off during the storms, then the drivers are left unprotected. Again, the way to troubleshoot this is to FIRST verify that the interface in the board is operational before blaming the distribution box.

Only possibility is from Aviom parts dept. I assume you have one physically broken and NOT just an inoperative one which the key itself would be OK and the contacts would be dirty or bad which is a different procedure.

First, try plugging them into another device to make sure the problem isn't the headphone jack on whatever system you are using. If you determine that it is definitely a problem with the headphones, the problem would likely be a wire broken away from the plug. If you have sound on one side and not the other, the culprit is one of the two signal wires. If you have no sound at all, the ground wire has probably broken away. The beak could either be at the plug end, at the headphone end or somewhere along the cable.

If the headphones are still under warranty, you can likely return them for a new pair. If not, the plg or the entire cable may have to be replaced.

Check if headphone jack also has right channel dead... If headphones work on both channels, switch contacts on headphone jack MIGHT be the problem.