I have been scratching my head for a fix for Cortana who wasn't responding to my voice commands nor my "Hi Cortana" greeting, and finally I got a fix for Windows 10.
Here is how I did it.
- Right click the speaker tray icon
- Select recoding devices
- Select the microphone
- Select enhancements
- deselect the "Disable all sound effects"
Cortana then worked fine after this tweak. Hope it helps.