A broken wax motor can potentially cause issues with the operation of a dishwasher, but whether it will stop the dishwasher from starting depends on the specific model and design of the dishwasher.
Wax motors are used in some older dishwasher models as part of the door latch mechanism. The wax motor expands when heated, which helps to release the door latch and allow the dishwasher to start. If the wax motor is broken or malfunctioning, it may not be able to properly release the door latch, preventing the dishwasher from starting or functioning correctly.
In more modern dishwasher models, wax motors have been largely replaced by other types of door latch mechanisms, such as solenoids or electronic switches. If your dishwasher uses one of these alternative mechanisms and the wax motor is broken, it is less likely to directly impact the dishwasher's ability to start.
If your dishwasher is not starting or experiencing other issues, it's best to consult the user manual or contact a professional appliance repair service to diagnose and fix the specific problem. They can accurately identify the cause of the issue and recommend the appropriate solution or replacement parts.