Ok, I'll try to make this simple. Forget that the controller works two functions, boom lift and swing, lets focus on boom lift. Flip your lid open, engine not running, work the boom up/dwn lever so you can identify which shaft is operating a micro switch on one side and the potentiometer on the opposite side, those are the two components you want to focus on.
The micro switch sends a voltage signal to the circuit card mounted in the platform control box, this signal "powers up" the circuit card so it knows you're working either boom up or boom down. Now that the circuit card knows you're operating boom it needs to know which direction you want to go, up or down, and how fast (proportional speed), that's the information that the potentiometer sends to the circuit card. The swing circuit works the same way.
The test objective is to get a preliminary diagnosis of whether the problem is with the controller components, or with the circuit card. Assuming your swing operates proper, which I assume it does as you only have a problem with boom operation, we want to connect the boom circuit card to the left/right operation of controller and connect the swing circuit card to the fore/aft motion of the controller.
To do this you have to switch connections to the micro switches, connector should be at terminals of micro switch, then switch connections to the potentiometers, connector should be in the wiring harness between potentiometer and circuit card.