No internal speakers and no headphone sound with iMac

Suddenly and from one day to the other I have no more sound coming from the headphones output on my iMac and in the system's preferences no internal speakers are shown anymore.

I do have LogMeIn installed and it can be selected as output, the sound also works remotely.

When I play a youtube move in system preferences one can see that audio is registered so it does come in.

When I stick the headphone jack in, system preferences does not show the headphones either.

I tried resetting Pram, SMC,

repaired permissions several times,

stuck a tooth pick in the output port, wiggled it,

stuck a headphone connector in multiple times,

stopped several processes related to audio through the activity monitor,

restarted several times,

used disk repair,

removed audio preferences,

looked if the sound was set as mute,

but nothing helps to solve this issue. 😕