hello!
We have a Blue Robotics motor that works when directly connected to power, but when connected in circuit with the ESC that came with it, we cannot get the motors to work using an external controller. We’ve checked that all components of the circuit work individually, but we can’t get our motors to work when in circuit 
@Ellie,
When you say: “We have a Blue Robotics motor that works when directly connected to power,” what do you means by “directly connected to power”?
Do you mean that you are powering the motor with an ESC that is separate from the ESC that came with the motor? These are brushless motors and not brushed DC motors.
To correctly control the motor, it must be attached to a brushless ESC and power applied to the ESC along with a PWM signal from an external source. At startup the PWM signal to the ESC must be set to 1500us so that the ESC can determine where neutral (stopped) is.
Regards,
TCIII AVD