I started researching this problem and it seems that there can be several reasons why this can happen. It can be a bad heating element, a bad thermostat, a bad motor for the steam vent, or a problem with the drainage system. After looking into this, I suspected that it was a bad heating element.
To check this, I was going to get out my multimeter and run a continuity test on the heating element. The problem was that I would have to disconnect the dishwasher and lay it down to gain access to the heating element connectors. With this dishwasher, it takes a while for me to disconnect it since there is very little space to work in underneath. So, I decided to visually inspect the heating element thoroughly first.
As it turns out, I was able to see right away that there was an issue with the heating element. In these pictures, you can see the element had a burnt spot that didn't look like the rest of the metal.
I'm not sure how this happened. It could have been when we had a plastic cooking utensil melt during a washing cycle after it fell from the rack onto the heating element.
Seeing this issue made me feel confident enough to order a replacement even without a continuity test first. The new element arrived yesterday since I paid extra for priority shipping. To get my money's worth out of the extra shipping cost, I went ahead and installed the new heating element on the same day.
Here's an image of the new element with the bad element removed. The new heating element still has the sticker and packaging material.
With the bad heating removed, I was able to run a test on it to confirm that it was bad. In the following picture, the needle on the multimeter should be close to 0 (the right side of the multimeter) to indicate a good test. As you can see, the needle is on the left side of the multimeter which proves that there was a problem with the old heating element.
Even as I was handling the old heating element, I noticed that the metal was broken at the spot pictured above and it took only minimal force to split the element into two. So, I guess I didn't really need to run a continuity test but it was just for good measure.
Cost of the repair: $17.95 (plus shipping)
Cost of a new dishwasher of equal value: approx $500
