Start with checking the supply voltages with a DMM, and check for AC ripple on the supply. Or, get a cap kit and replace the electrolytic caps on the sound board. That's most likely the problem, dried out aged capacitors. Beyond that, get an oscilloscope and troubleshoot. The schematics have some waveforms indicated as good starting points for that process.

While replacing the caps is not a bad idea I don't think this is a capacitor problem. Sounds like the sustain circuitry is not working and certain notes sustain on forever.

Check the 560-3 repair manual, section 4 symptoms 1 and 2.
http://arcarc.xmission.com/Pinball/PDF%20Pinball%20Misc/Pin%20Repair.pdf

Over adjustment or even bad sustain pot can make a never ending noise. Twizzling the vol pot might just be adjusting the audible noise from a sustain problem in and out.

The board should chirp during the MPU's power on self test. Since don't hear that either a few things might be going wrong. The header pin solder joints on these single sided PCBs with no plated holes are extra prone to cracking.

If you want to try and fix it. Follow the Bally 560-3 book and/or Oliver guide and you should be able to get it going. 560-3 book in link above. Here is oliver's write up. http://www.pinball4you.ch/okaegi/rep_soundold.html

There are new replacements available from http://nvram.weebly.com. They are in the USA but will ship to Europe