Okay, I am back and let's see if we can get you dried up
Peter B,
Welcome to the site here.You will find us all very helpful and willing to teach you along the way too.
First, do like Sudsmaster suggested if you have an air gap on the sink top,make sure it is clear and free running even though they are rare to see anywhere in NY!
You need to check if the drain hose is kinked in any way which would restrict the water from draining and would also contribute to food particles getting stuck in the hose. If you can, remove the hose and inspect it.Then you can run a rinse and hold cycle and then drain the dishwasher into a 5 gallon pail or bucket of at least 2 gallons in size.You will see if the machine draiins completely or not.
It is entirely possible that your sink drain could be slow and you will cause a back pressure to prevent the water from draining completely too. My aunt had that problem all the time with her KDS18.
The 18,19 and 20 also had a relatively small drain impeller in them and with the age of your machine, the pumping vanes on it would have worn down a bit as well. I always advise anyone who has those models to purchase a shaft seal and drain impeller kit from HOBART not Whirlpool since I know for a fact that the drain impeller has much larger pumping vanes on it and will really drain the sucker dry.
If you want the part number just let me know and I will give it to you. It really makes a world of difference too.
One other thing to check is the drain solenoid valve under the machine. It is electrically activated and you know when it is operating by the loud snapping noise it makes when it is energized. You should remove it and see if there is anything caught up in it that would prevent the water from passing cleanly thru it.You will be shocked at what can get into the bottom of a dishwasher and prevent it from draining.
Make sure you have run the cancel/drain cycle at least once if not twice to get as much water out of the machine as you can. Then TURN OFF THE POWER TO THE MACHINE!
There are always live components and wires under the unit which could hurt you so don't do a thing 'til you shut the breaker on it.
You can then remove the black kickplate and the lower panel and you will see the white valve with the red coil on it with a pink and a white wire attached to it and two hoses clamped to it. That is the drain valve. Unclamp the hoses to it and take the wires off and have a look inside and see if there is any crap in it. you will need a pot under it for the water to drain from the two hoses.
If there is debris in it, there is your problem. If not, then the hoses or the impeller is the problem.
Let us know what you find.
And sorry for the delay. I was in Arizona for the weekend and had no computer access.
Good Luck!
Steve