The detergent cup in your dishwasher opens automatically when signaled by the timer control. If the detergent cup does not open, it is most likely to be one of three things.
If it is gummed up with detergent grime; it may simply need to be cleaned. Usually the washing action of the dishwasher is enough to clean the dispenser, but detergent may have gotten into the workings and requires interior access for cleaning.
Many dishwashers use a bimetal switch to electrically trigger the detergent cup to open. When current is applied to the switch, the metal in the device moves and allows the detergent cup to spring or drop open.
Finally, if it is not receiving the signal to open, that suggests a problem with the timer control or the wiring.
Before replacing the bimetal assembly, unplug the dishwasher or shut off the power at the fuse box or breaker panel to avoid an electrical shock hazard.
To service the detergent cup and bimetal switch, it is necessary to access the interior of the door. Access varies by model; on some models the interior panel is removed, on others, the exterior panel. It may be possible to simply remove the decorative front panel by removing the a retaining clip or strip along the top, sides or bottom. However, often access is more involved as described on the next page.