Gearandsuch, I have the same problem with figuring out electric stuff. My local sewing machine repair shop will do a 5 minute diagnostic for $15.00.That's what I would do if faced with your problem.
I have no idea how much you have invested in this 403, but the problem with the machine seems to be beyond your capability. Have you considered parting it out and buying another machine? Even if you finally figure out it's the motor, can you replace it yourself? Can you rebuild the motor yourself? How much will it cost to get a used motor? How do you know if the replacement motor is good? Is it worth buying another controller just to test your machine or maybe borrowing one?
I assume the 403 has the same electrical setup as the 401, in that the controller plugs into the machine and the "wall plug" plugs in at a different spot. The controller itself is generic and can be replaced, but you will have to use the cord that came with the 403. I don't know if you can buy a controller that is already wired to fit a 403 or not. All in all, it might be easier just to wire your cord to a controller from another machine. That would be easy to do if you have one available. Just follow the instructions of a youtube video for adjusting a controller/foot pedal.
I'm sorry if this is kind of rambling, but these are the thoughts/questions I have about your problem. I'm not an expert, but I have adjusted a controller. I would not tackle replacing a motor or rebuilding a motor.
bkay