FLS hit the nail on the head and actually helped me with my Vox issue which was not quite the same...
Double check a few things:
1) First verify in Windows what your default microphone is set to. In my case I had the microphone accidentally set to my USB Webcamera mic however in the actual game it was set to my USB Headset mic but not working for some reason. Make sure your Windows mic and AHIII mic are set the same.
2) Try FLS's suggestion in offline mode and tune your radio (channel 5 or V) to SERVER. Then while you still have the radio list up try to key up (assuming you have transmit tied to a button on your joystick) and see if you actually show transmitting. If not, you have some other issue going on with you transmit button assignments.
3) To reset Vox try the .resetv command. There are 3 options using this command to reset the various vox components (so for example .resetv 1 or .resetv 2 or .resetv 3). Once you've done this, again try your vox in offline mode and see if you can get it working there.
Good Luck!
Cheers,
Elec1