I had a situation once where I had full power at a fuse panel, but when I turned anything on it would not run. I was able to measure the power on a fuse clip, 12V with no load, then less than 2V with a load. Eventually I found that the fuse panel power feed multi-strand wire had two good strands left out of about 20. As I finger traced the wiring, it broke when I touched it. 2 strands were shiny, and the rest had a heavy patina.
The point is that measuring voltage is only half the equation - you need "power" to run the motor, which in this case is voltage plus amperage.
Can you measure the voltage when it is trying to run? This may point to a corroded contact, bad connection, or a wire situation like mine.