Almost answered your own question!
When the machine is in the dry portion of any cycle except the rinse and hold cycle, the fan should be running all the time.(The fan does sometimes turn on whle the r/h cycle is advancing to the off/reset position on some timers)As you said, the energy saver button simply shuts off the heating element. If the fan did not run and the element comes on, you should get some smell like a very hot electric heating element smell. There is an over heat protector on the dryer assembly which may be turning the heater off so maybe no smell.
I would pull the machine out and try to turn the blower by hand. If it turns that is one hurdle.then you should look to make sure that all the wiring to the blower motor is intact and not broken or that one of the crimp on connectors has not come apart. KA never really used great connectors and after this many years, any of them could have corroded enough to break off or lose their connection.
If all looks good then the motor itself may be shot. Again if it is the original, anything could have caused it to fail at this point.
Now, if the fan is stuck, and the motor is still actually good, the motor itself will shut off by thermal protection as well. You may be able to get the motor turning again by lubricating the bearing housings with some light oil like 3 in one for electric motors. It is non detergent and really light. The bearings are just brass bushings that absorb oil from the cotton wicking inside of the housings and are probably dried out. Try moving the blower wheel after a few minutes of soaking and you may get some more life out of the blower and motor.
Trying all these tricks is easiest if you remove the motor itself from the housing. It is held in with 2 screws and has keyhole slots to rotate the motor free of the housing.
You will need to check the little thermal protector with the two terminals on it that is screwed to the housing.If you know how to use an electrical test meter, it should show a closed condition at room temperature. If it does not, then it is open and the heater will not heat(assuming the heater is still actually good). You can test the heater using your ohm meter as well and should show a small resistance when you connect the leads across the heater element connections(2 tabs on two ceramic blocks with the supply wires removed.
As Ralph said, the Sheath heaters will give a sizzling sound when heating the water in the last rinse especially because it is pouring 1400 watts thru that water. As soon as it finishes filling for the final rinse, check your water level. It should be above the element and just a little bit of the way on to the bottom of the tank itself. The final fill is less than the main wash and rinses so do not expect to see it nearly as high as the top of the filter. If it is significantly lower, then you have a fill valve problem and this will affect all the fills and rinses on all the cycles. I don't have the fill chart handy to tell you how many qts each segment requires but somebody will probably chime in and let you know.
BTW, the machine DOES also delay for a short while in the final rinse fill even whn you don't select "Sani" cycle but will only delay for a short amount of time and then continue the cycle regardless of the water temp it sees at that time.
The small drips you saw, are not worriesome as the black rubber piece is called an evaporation channel and lets any small drips accumulate there to dry. If you are still seeing water above the galvanized panel where you showed the drip location, make sure that when you put the outer panel on that it sits in the little rounded out area of that channel. It will help seal the moisture out of the door cavity. Also, make sure that the rinse dispenser is not leaking from the gaskets in the tank or from the dispenser itself.
Hope this helps. Lots of little nagging things happen when machines are this old but it is fun and satisfying to find the problems and fix them.