Hi @thesilverfox51 ,
If you have access to a DMM (Digital MultiMeter) use its’ Ohmmeter function to test the continuity of the right speaker wires from the aux cable plug through to the right speaker.
I realize that you have tried different cables but it is easier to test with a cable inserted into the headphones. Having the earphones dis-assembled - at least the side where the aux cable plugs into will speed things up.
Plug an audio cable into the headphones only. Set the DMM to measure Ohms (200 Ohm scale) and then place the Ohmmeter’s test leads between the tip connector and sleeve connector of the aux cable plug at the other end of the cable which is inserted into the headphones. You should get a reading as you are “measuring” the left speaker. This is just to prove that you have set the meter up OK.
Next place the meter test leads between the ring connector and the sleeve connector of the aux cable plug. From your description you will not get a reading.
Then you need to do point to point testing. That is place one meter test lead on the ring connector and use the other meter lead to see if you can get a reading on the aux jack socket connections in the headphones.
You may have to identify which aux cable jack socket connection is the one for the ring connector. The easiest way is to identify the tip connector by placing the meter probe on the tip connector of the cable plug and then “find” it on the socket connection, next do the sleeve connection the same way. the one that is left is the ring connection.
It may be that the internal connecting spring in the aux socket in the headphones for the ring connector has lost tension and is not making a good connection to the cable plug.
Unfortunately if this is the case the socket cannot be repaired it has to be replaced.
Here’s an image which shows how audio stereo cable plugs are wired:
(click on image to enlarge for better viewing)