This issue (essentially a "silent Siri") appears to be prevalent with many iPhone 6 devices running iOS 9. Which language are you currently using Siri with?
A full restore of the iPhone may not be necessary. First, invoke Siri and ensure the volume is turned up.
Next, please can you attempt resetting the Network Settings first, by visiting:
Settings > General > Reset > Reset Network Settings
Please attempt to invoke Siri after resetting the Network Settings. If this does not solve your issue, you may need to reset all device settings (your apps and data will remain unaffected).
To reset all device settings, please visit:
Settings > General > Reset > Reset All Settings
Unfortunately, if these minor resets are unable to alleviate the issue, I would advise a full restore of your iPhone, as this appears to be the sole remaining solution.