Unfortunately, the law of converse logic does not apply to this case. If the audio switches were also non-functional, it would have implicated the spiral cable, but working audio switches do not necessarily indicate the spiral cable is OK. It only takes one broken conductor in the cable to kill all of the steering wheel HVAC controls.
Toyota service info I have does not disclose if there is a separate connector in the steering wheel for the HVAC switch cluster. The other connectors between steering wheel and HVAC controller are all multiple-pin. If disconnected, something else would also be affected. So I think the unplugged connector scenario is at best a long shot.
If possible, you might ask the previous owner if any part of the steering wheel was recently removed (possible driver's air bag replacement?). It's easy to forget to make a note of the wire routing, and pinch/damage a wire during re-assembly.
You now know roughly what it would cost for a replacement part . . . all 3 possibilities are in the $200 - $250 range (plus shipping). Perhaps this gives you some negotiating leverage.