I had the same trouble with my computer. I could hear sound but wasn't able to say anything.
Our computer is weird, it does the stupidest things for no reason.
Anyway, the computer got some horrible virus so we took it down to a shop to get it fixed, we also got more RAM and a good clean out (lots of dust and crap). After that, my headphones worked and most of my flight sim addons.
God knows why the headphones started to work??? I didn't think RAM would help. Maybe the dust was causing something to short out.
So, if your computer is like mine, it might just need an upgrade. The headphones might not be the problem.