First, the Arduino bits and the VCO are almost entirely separate, so you may want to focus on one of them at a time – I’d start with the VCO.
I assume you have a multimeter? First thing to do is to measure the DC voltages at the 3340 supply pins, and the CV voltages on the various 100k resistors that lead to pin 15, relative to ground.
I should do a drawing for the #1222 PCB, but in the meantime this annotated stripboard might help you locate some measurement points:
When powered on, pin 3 should be −7.2 V or thereabout, pin 12 should be 0 V (GND), and pin 16 should be +12 V.
Pin 15 is the CV input, which is 0 V too if you measure it, held there by the internal summing amplifier, but you can measure the total CV by measuring on the other side of the 100k resistors that lead into that pin, and summing up the values (at A or B in that picture, but these are elsewhere on the #1222 PCB). You want at least a few volts there in total to get an audible signal (see here for more).
The values to the left are resistance values, and should be measured with the power turned off. You can measure directly between the 3340 pins on the #1222, i.e. pin 1 to 3 should be roughly 30k, pin 2 to 3 should be 5.6k.
EDIT: Spelled out the expected voltages here as well.