rptort:
Also, should you not include some sort of resistor divider between +5V and GND to put some DC bias on the OPs' inputs? And for that matter, a voltage higher than GND on the inverting amplifier's non-inverting input - because otherwise, it will not amplify well.
The input signal from the MIC is both positive and negative, so I'm using two OPs (one inverting and one non-inverting) to amplify the positive and negative "halves" of the signal. Then, I sum them in the microcontroller.
Why it works on breadboard?
I attempted the breadboard again and it didn't work (no idea what I did last time when it worked). I continued experimenting by placing a 10k pot on each SPI line and discovered that when any of the SPI pins are at ground or +5V, the programming doesn't work. But anything in between, everything works fine. If that holds true, then with no input, the non-inverting OP is holding the USCK line at ground which could be the issue. Thoughts on that?
use resistors in the range between (just an educated guess here) 220 and 4k7 Ohms. Between the OPs and the controller, that is
You mean like this:
Yep, the resistors go right there.
I wonder though, is there a reason you are using different amplifiers for each half-wave? As I said, with a DC bias, you could get the full wave through one amp and detect it with a single ADC channel. One difficulty might be increased high-pass frequency, but the right choice of resistors should offset that. Your system as it is is a bit non-linear actually. The non-inverting amp has a gain of 11, the inverting one a gain of 10.
And driving an op-amp input with a voltage of less than its low supply voltage might actually result in undefined behavior. The OP should pull the differential input voltage to almost zero, yes, but there still has to be a minuscule tad of voltage between the input pins, meaning the inverting input still has a voltage below GND. Have you checked the datasheet whether the amp still works? Have you tested the circuit?