Things to try:
1. Make sure you have bound a push-to-talk key and have the right key pressed while talking.
2. Make sure your microphone is plugged in and enabled by your operating system.
3. If you are running Mac OS X, make sure you have enabled access for assistive devices or push-to-talk functionality will not work.
Enabling Access for Assistive Devices on Mac OS X
Go to Apple at the top of the screen and choose Software Preferences...

Choose Universal Access

Make sure Enable access for assistive devices is checked.

Close Software Preferences.
You can get further help by posting on the official Imptalk Forums.