Looking at the wiring diagram and solenoid schematic page 2, the switch triggered solenoids are controlled here.
IC6 should be tested and confirmed working.
Do you have a logic probe? It's possible to confirm that IC6 is bad or working with a logic probe.
Start a game, probe the output pins of IC6 at pins 3, 8, 11, and 6 while simultaneously closing the switches of left and right slings, and the pops. Any output changes at those pins?
If IC6 checks out, move on to testing IC8, IC9 and IC7 with logic probe.
switch-trigger-solenoid (resized).JPG