No audio device detected in system report (liquid-damaged Mac)

I adopted a liquid-damaged MacBook Air which was completely non-responsive.

I took it apart and saw signs of liquid intrusion, with some corrosion around the I/O ribbon cable connection (mostly on the logic board side but both needed cleaning). I tried cleaning the existing cable and connectors and managed to get it to boot, but not charge.

The cable looked like it caught the worst of the corrosion so I replaced it and now the laptop works normally aside from not detecting an audio device (About this Mac > System Report shows no audio device: audio controls are greyed out in System Prefs).

I’ve reset PRAM just for fun with no results. So, no speakers, no headphone, no mic, no nothing related to audio.

Can replacing the I/O board possibly solve this problem, or is the core audio logic on the main logic board? I couldn’t find a definitive answer to this so I thought I’d ask the Fixers…