[Debezo]

In this case, we use "声が出る/出ない(koe ga deru/denai)", "senshuu byouki de koe ga denakatta".
But "hanasu koto ga dekinakatta" is ok. And it's better to just say "byouki de" rahter than "byouki ni natta kara(node)" or "byouki datta kara(node)". The latter are a little verbose.

To nijiro, You are right in naru. It can be "koe ga denaku natta" or "hanasu koto ga dekinaku natta". But inai(iru) is used with animate being, isn't used with voice.