The start button on my kenmore dishwasher doesn't work anymore.

Check the switch with an ohm meter after cutting power to the unit. When the button is pressed the ohms should go to zero, or close to zero. If the switch is good then the problem is elsewhere and you will need the model number to get a wiring diagram. The dishwasher has safeties and other relays that can fail and prevent it from responding when you press the start button, which rarely fails. DrTom4444