Sound is generated on the primary logic board and transformed to analog (what goes to the three.5mm jack through a DAC (Digital Analog Converter). There may be additionally extra circuity close to the jack that handles this audio.
It’s seemingly you fried this. To see in case your sound chip nonetheless capabilities, go into the System Profiler and search for the audio adapter. If it exhibits particulars, it means it’s nonetheless purposeful and solely the circuitry at or close to the jack has failed.
You can doubtlessly get this repaired, however you’d be higher off getting a USB Audio Adapter or a Bluetooth headphone. It will likely be inexpensive snd the standard a lot better (relying on the standard of the gadget you buy).