This could be "capacitor plague" on the controller board. TVs and computer monitors are the most common items with this problem, but I've seen it on a dishwasher with the same symptoms you describe. The capacitors are burned out inside, and the top of the capacitors may be domed upwards from the internal pressure from the overheating. (Smaller electrolytic capacitors may have the outer can pushed partway off of the rubber lead seal instead.) See the photo below to identify a bad electrolytic capacitor. Often more than one will be bad.
Fortunately, replacement capacitors are relatively cheap and easy for an electronic technician to replace (any TV tech should be able to solder it in). There are five parameters needed to specify a replacement capacitor:
Capacitance in uF (the "u" is actually the Greek letter mu, for "micro"), as in 470 uF. You must match this number.
Voltage rating. The new part must have a voltage rating at least as high as the original. This will probably be 6.3, 10, or 16 Volts.
Temperature rating: the maximum temperature must meet or exceed the rating on the original; the minimum is not so critical because you won't operate or store the dishwasher in sub-freezing temperatures.
Physical size: the lead spacing should be the same as the original, and the capacitor should not be too large to fit in the available space when the board is installed in the dishwasher. Usually these dimensions are in millimeters.
Ripple current: this is not marked on the capacitor, but getting a new part with too low a ripple current rating will result in replacing another burned-out part before long. Generally, the Panasonic FR series capacitors have a more than adequate ripple current rating. Often it is worth going one size up in voltage to get the extra ripple current capacity and lifetime rating, if the part isn't too big to fit - the price difference is a few pennies.
(Photo from the-computer-problems-guru.com) Note the difference between the marked bad capacitors and the good ones with flat tops. The part with stripes is a resistor. It may get hot during operation. Replacement capacitors should not be touching any large resistors or they may burn out prematurely. It is very important that the new capacitor have its polarity marking stripe going the same way as the original; putting it in backwards will ruin it and may even cause it to explode.
Note: disconnect power from the dishwasher before opening the control panel. Do not touch the circuitry with your fingers; only handle the circuit board by the edges. Touching the circuitry may damage the parts with a static electricity discharge, even if you don't feel the spark. If you need to take the board out for repairs, get an anti-static bag to carry it; do not use an ordinary plastic bag. If nothing else, put it component side down on a cookie sheet, and again, avoid touching the circuit traces or letting them come into contact with material that could generate or conduct a static electricity discharge.
