One switch should not affect power to the other switches. My guess would be that that wire is not making good contact in the "multi wire connector". A voltmeter should be able to tell you which wires have voltage and which do not. One of the 12 vdc light probes with a sharp point you can penetrate insulation without hurting the wire is great for that kind of troubleshooting.
https://www.amazon.com/Voltage-Conti...52187988&psc=1