Keeps running will not cycle - Siemens SL85A705UC 24 in. Built-in Dishwasher

drain pipe is clogged and cycle programmer is faulty.

If you cannot cancel the cycle then turn power off and back on.
Then try to program a short cycle from panel and see if it works.

I am assuming when you say that it keeps running you mean the water keeps churning and does not drain out.
If short cycle works ok then the dishwasher is not heating water to the correct temperature. Need to check thermostat or heater.

if it fails to stop running only at the rinse part of the cycle it is probably in the timer as the solenoid valve has to cut the water off when the washer fills for the wash cycle too. fills for wash cycle and cuts off water, washes and drains, refills for rinse cycle and water just keeps running? does this every time you run it? that's in the timer. bad solenoid (water inlet valve) would keep running even on wash fill up. hope this helps.

The drier works fine and heats during the cycle and then when the cycle is over the heat quits but the drier keeps running? Does it shut off when you open the door?

I would put bleach in the detergent slot, run through each cycle. Then run the cycle again with just water. These are really touch when using detergent. Just a little bid of suds sets these things off.

Your water inlet valve either is stuck open or not getting signal to close from control board. I would check your inlet valve first.

If it runs o.k. at 50, I'd say check thermostat.

There is a recall on the control board of many of these models. I have written a guide to help. It is here. Look for the phone number near the top.

Your water inlet valve is sticking which means that it needs to be replaced. You can get it at your local appliance store or at repairclinic.com

you have a faulty float switch and possibly timer