Microphone preamplifier doesn't give expected gain
1.8 k&Omega; seems rather small for a electret pullup, especially to 9 V.  Have you checked to see what the datasheet recommends?

You are actually asking for a gain of 6800 in the passband.  I can't even guess where your 7.8 figure came from.  This is bad idea for a single stage.  Even at 400 Hz you are asking for a overall gain*bandwidth 2.7 MHz, so the opamp needs to be good to 10 MHz or so for the feedback to have some headroom.  You should only need a few 100 to 1000 gain from a ordinary electret microphone to line audio levels.

6.2 M&Omega; is really high.  I didn't lookup that opamp, but even if its input impedance is significantly larger, there can be other noise that gets into the signal at that impedance.  Just leakage thru dirt on the PCB can be significant.

With such a large gain, this configuration will take a long time to stabalize after power up.  The (R1 + R2)C1 time constant is one minute!  And, you would need to wait a few time constants for the system to settle close enough to the final operating point.

The high pass rolloff frequency set by R2 and C1 makes sense for audio, but the low pass rolloff set by R1 and C2 is 380 Hz.  Is that really what you intended.  Personally, I'd probably leave off C2 altogether.