[nijiro]

Edit: My translations here aren't 100% correct, check further down... I'll leave them up so that you can see my mistake and understand it too.

n'desu can be used with pretty much anything. I'm sure they'll explain in better in your class than I ever could, but anyway, as for your sentence, since it refers to a condition that was obtained, I would use the verb naru/narimasu, or "become". Basically what you might want to say, literally, is, "(it seems) I became not have voice."
Like:
Senshu watashi wa byooki datta dakara koe inai nattanda.
”Last week I was sick and so I lost my voice　(became voiceless)."

Koe here is "voice".

Or if you want to say, "I became can't talk", say:
...dakara hanasu koto dekinai nattanda.
"...and so I lost my voice (became inable to talk)."

You could also actually say "my voice disappeared", which is:
...dakara koe ga kietanda.
"...and so I lost my voice (my voice disappeared)."

I'm not sure how the Japanese would express a lost voice, but you could use any of these examples and be understood, although I would recommend being a little more formal if it's on your homework. ;P

先週私は病気でしただから話すことができないになった んです。
Senshuu watashi wa byouki deshita dakara hanasu koto ga dekinai ni natta n'desu.

That is how I would say it to be totally proper. (EDIT: I'm sorry if this sounded wrong, what I meant by "being totally proper" was just that I recommend using -masu forms instead of plain forms to be really proper, but you don't have to do it. Don't use this cause it isn't a correct translation!)

Please correct me if it's wrong!