This problem could manifest as the dishwasher running nonstop and not entering the drying cycle. Academy Fellow john63 points us in the right direction:
Check the continuity of the HEATING ELEMENT with a test meter---if "open" replace the HEATING ELEMENT.
If "good"---it's very likely that the HEATER RELAY---located on the right side of the dishwasher at floor level---has failed.
During the DRY CYCLE---there should be 120 volts AC coming from the HEATER RELAY---to the element.
Most HEATING ELEMENT or HEATER RELAY failures occurred in homes that had a "Tankless/Instant Water Heater".
Other possibles are:
1) One of the DOOR SWITCHES FAILED
2) MAIN BOARD (very rare)
Heating element ==> http://www.repaircli...Number=DMR78AHS
Heater relay ==> http://www.repaircli...1000260/2028620
Door latch ==> http://www.repaircli...400002B/1603323
Main circuit board ==> http://www.repaircli...Number=DMR78AHS