I had this issue with a Kenmore 665 series. I checked the heating coil and it was reading between 8-30 ohms. I checked the thermostat which had lost to 0 ohm resistance as well. The control board was working okay. I ended up running it into diagnostic mode and this made the coil heat up properly. Diagnostic mode is accessed by pressing any 3 buttons in a row 3 times (1,2,3, 1,2,3 1,2,3…). Do this with the door open and press the buttons in a row 3x. All the lights will turn on, then close the door. Over the next 12 or minutes the dishwasher will check all of its sensors and reset everything, including the heating coil. There is an internal safety mechanism that will shut off dishwasher heating for various reasons. So step 1 should be to run diagnostic mode. Then check the coil for damage then resistance, then the thermostat. Also make sure the dishwasher has jet dry and a good hot water setup. This will help with having dry dishes.