Try a precision full wave rectifier feeding a comparator with a reference set by a pot. This will give a logic level output you can poll using the PIC. When it's high, enable the amplifier, when it falls low activate your white noise burst. Try generating random numbers (8 bit) and feeding them to a 2R2 DAC, you could even just switch a diode noise source output into the amp input.

I did somethineg VERY similar for a company as a water leak detector. A microphone listened for a noise in the pipes then activated an alarm if the noise was of a certain type and exceeded a certain duration.

Hope this helps