The 18.6v reading is probably due to being powered on AC. A 18.6v system voltage reading for a 13.5v boombox powered from the mains is not at all uncommon. I have seen Sanyo M9994's (12v boombox) read 19 volts when powered by AC with no load.
Oldskewl: I would suggest at this point that you simply pass this boombox off to a technician qualified to do the repair. The fact that you weren't even able to take a simple voltage test suggests to me that you don't really know what you are doing. This is a 4-wire motor. You said no power at the motor. I have little confidence in your test method to determine voltage at the motor. How did you test for it? Also, what you are looking at is a wiring diagram. The one you should be using is the schematic diagram, which is a far more useful tool to see the circuit path at a glance. If you can't determine whether or not the motor even has voltage, there is no reason to mess with the variable resistors. That variable resistor does not control voltage to the motor.
Don't take this the wrong way. This is not intended to be a knock on your diagnostic abilities. Not everyone is a rocket scientist -- I sure know I'm not. That's why I leave the rocket designing to the scientists. In your case, you don't have the basics down yet and without the fundamentals, it's really hard for others to help you since the fundamentals really helps you to follow along. You are right, it's not that hard of a circuit, and what I told you before about starting at the motor and working your way back -- the diagnostic process really IS that simple. There is some circuitry between the motor and the switch, right? YOU have the boombox. YOU have the schematic or other assistive diagrams. YOU are the man on the spot, so this is something you really need to do on your own. Unless we are also looking at and have that boombox in front of us, and/or the diagrams, all we can do is provide you with general guidance. When we say trace the circuitry between motor and switch for continuity, you must be able to do that on your own since without the schematic and boombox in front of us, how can we give you step by step? EVERY boombox is different. Even if I worked on that exact model, on that exact issue 6 months ago, how could we possibly remember?
BTW, if this comes across as harsh, don't take it personally. Those that know me, also understands that I probably have as much tact as a tree.