It should be behind your converter. When I say this, I mean that if you actually remove the entire converter from the wall, you should find it behind there.
Sorry, assumed you had a combination distribution panel/converter. So you've already looked behind the distribution panel then?
When transfer switches fail, especially through arcing, they tend to do all kinds of nasty things to the wiring, but fortunately it's generally confined to the transfer switch box itself. Sometimes they take out other electronics though, so yes it's possible. What control box are you referring to though? Are you referring to the converter or what?
Your generator has a 20A DEDICATED circuit strictly for one of your air conditioners. This circuit does NOT go through the transfer switch.
So what I think is happening is that obviously your transfer switch has failed, which has eliminated all your 120V, EXCEPT for the one dedicated air conditioner.
So, everything will be normal I think once we find that blasted transfer switch and replace it.