Karl, how are you testing for a continuity break between those capacitors and the IC inputs?? It would require a board fabrication error, or faulty soldering on the capacitors or ICs to cause such a fault, so while certainly possible, it seems unlikely.? It seems more likely a measurement error, perhaps a layer of flux on the capacitor terminal or IC pin preventing good contact of the probe?
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And no, such a fault would not render IC407 with no signal to process.? Each of these is a feedback capacitor, which helps stabilize and improve the performance of the amplifier - so yes, it is an important part of the circuit to keep performance high, but it would not inhibit the signal from going through and being amplified.
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Stan KC7XE