Mic Amp Mixer and Audio Distribution, Won't Work! Help! (Update 2) (Solved!)
First question : What kinds of microphone? Common electret mics may need a bias supply, 1.5 or 3V fed through a 2 k to 10k resistor to bias them. (If you add this, also reverse the input coupling capacitors to their +ve terminal is positive!)

Second : what variety of opamp are you using? The +ve input is connected to ground via 1 megohm. The -ve input, via 1 kilohm. If the opamp is a type with significant input bias current (as low noise audio opamps usually are) this impedance imbalance introduces a significant input offset voltage ... multiply that by 100 and the opamp output may be sitting at a supply rail, clipping the signal. This is easy to diagnose with a DC voltage measurement on the opamp output. Reducing R2 to 1k would help (but load the microphone). Reducing the gain at DC, e.g. with 22 to 100uf in series with R4, R9,R14 would minimise this problem.

Any DC on the opamp output will create havoc with the faders RV1 to RV3 - loud noises as you fade... you probably want coupling capacitors between opamp and fader - OR reduce the opamp gains at DC as above, or possibly both.

UPDATE : Also, lose R20. It adds DC bias which would be important if the negative rail was 0V instead of -V, (i.e. single supply voltage) but if that was the case, all the other stages would need similar bias arrangements. ANd if it's an attempt to properly bias the electrolytic caps around that amp, ... well none of the other electrolytics have similar bias arrangements (and C12 is reversed!) As that stage also has a gain of 10, U2A output may be sitting at V+ at the moment (eliminating your audio signal)