When it calls for a drain cycle it sounds like the motor tries to start for half a second and then the display blinks and there is a click. This repeats every few seconds until you open the door. If you wait 15 minutes and close the door it will click once and then drain fine; until the next drain cycle.

Usually the sink connection is not an overflow, it is the main drain from the dishwasher. It is more likely your s-bend is blocked under the sink- try putting a bucket under it and unscrewing the u-shaped piece and cleaning out (remember don't wash it in that sink while the pipe is off)

Beneath some dishwashers, there's a timer-activated drain solenoid (an electro-magnetic coil) that opens a drain valve, to drain the wash water through a hose and out to the house's plumbing waste system.

Thermostat Dishwashers have one or more small, cylindrical thermostats. These are a bit larger in diameter than a dime and have two or more wires attached to them. They protect the dishwasher, dishes, and humans by turning off the heating element that heats the water or the air in the dishwasher when it has reached its pre-set temperature. The thermostat automatically re-sets when the temperature falls to a lower level.

Soil sensors Many of the more-recent dishwashers use multi-component soil sensors, which continually monitor the wash water during the wash cycle. These sensors help the dishwasher to wash for the amount of time that is appropriate for how dirty the dishes are, rather than for a pre-set period. When the water becomes clear enough, the sensor signals the timer to continue with the next cycle.

Door switch Dishwashers have a door (or door interlock) switch that--if properly functioning--shuts off the dishwasher when the door is open.

Drying fan Some dishwashers use a small fan to blow air (or heated air) into the dishwasher to dry the dishes faster. If your machine has a drying fan, it's beneath the dishwasher, usually in the back right corner.

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Is the door open or unlatched?
Make sure the door is completely closed and latched.
Is the selected cycle incomplete?
To drain while the dishwasher is running, press the Start/Cancel pad once. The dishwasher will drain, and then shut off. To drain while the dishwasher is not running a selected cycle, make sure the door is completely closed and latched, and then press the Start/Cancel pad twice. The dishwasher will drain, and then shut off.
Is there a new garbage disposal?
Make sure the knockout plug is removed in the new disposal. For many dishwashers, the drain hose is connected to the disposal. The knockout plug must be removed from inside the food waste disposer inlet.
Is the drain system blocked?
Run the disposer to clear the drain system.
Do you have an air gap at your sink?
Check to see if the air gap is blocked by foreign material. To clean the drain air gap, follow the cleaning instructions provided by the manufacturer. With most types, you lift off the chrome cover, unscrew the plastic cap, and then check for any soil buildup. Clean if necessary.
Is there a loop in the drain hose less than 20" above the floor?
Make sure the drain hose is looped so that it touches the underside of the counter before connecting to the sink drain or disposer.
Is there a kink in the drain hose?
Replace a kinked drain hose.
Did you reuse an existing drain hose?
Make sure to use the new drain hose that came with the dishwasher.
Is the sink drain clogged?
If the sink is not draining well, a plumber may need to be contacted. Most dishwashers connect to the sink drain. If the sink drain is clogged, the dishwasher can't pump out water.