Remove the door panel by removing the screws at the four corners of the dishwasher. On most Kenmore models, the screws are on the side of the door panel.
Pull out the two wires leading into the detergent dispenser's solenoid trigger and test them for continuity with a volt ohmmeter. Test the wires by first setting the meter to its lowest setting and touching the test leads together. This will zero out the machine. Next, touch the test leads to the metal or bare wire ends of the solenoid. If the meter moves toward the right side of the scale, then the solenoid still has good continuity and the problem is most likely buildup around the dispenser. If the needle stays toward the left side of the scale, then there is no continuity and the part needs replacing.
Order the replacement solenoid from Kenmore and install it.