Looks like you're not getting any bites in the Denial forum, so let me see if I can help.
How are you connecting the VIC20 to the monitor? The cable is the most likely cause of audio failure. Check the cable for continuity on audio, video and ground.
If you are using an RF modulator that's our second most likely culprit.
Do you have a composite video cable? The VIC20 can use the same cable as the Atari 800 and North American TI99/4A to connect it to a composite monitor. If you have a composite monitor with audio this will be much simpler.
If you look at the 5-pin monitor jack on the back of the VIC20, pin 3 is the audio line, and pin 2 is ground. This is line level audio so taking a line from pin 3 and passing it to any line-in, with ground to the shield should give you audio.
Below is an NTSC VIC20 motherboard, looking at the monitor jack from the solder side of the PCB. Pin 3 is the one furthest on the right
video monitor jack solder side.jpg 667.19KB
If you trace Pin 3 back you can see it goes to a yellow capacitor on the component side. You can see it here to the left of the VIC chip more or less in line with the cassette port. On my board is looks to be labelled C16:
video monitor jack component side.jpg 1.16MB
If you are still not getting audio with a composite cable, check that capacitor for swelling or leakage. Below it is a black transistor, which takes it feed from a resistor that traces back to Pin 19 of the VIC chip. That is where the audio is generated.
Trace along this route looking for damaged traces, dry solder joints or blown components. If you dont find anything and your VIC is socketed, you could try to lift it out and re-seat it.
Later CR VIC's have a simpler component layout but the pin numbering on the AV jack and the VIC chip is the same.
Edited by oracle_jedi, Tue Jan 8, 2019 5:59 PM.