This is my Mom’s dishwasher. I noticed a foul smell while visiting one day, found the washer had not drained. Checked all hoses and replaced the old air gap, all okay - nothing clogged.
Placed the drain hose into a bucket and ran the washer for a bit, then pressed the "cancel" button and the washer drained okay into the bucket.
Then ran the normal wash cycle and observed that the washer would not drain when going from "wash" to "rinse" or from "rinse" to dry". In other words, it won’t drain at all unless the "cancel" button is used. 
Any help or advice would be very much appreciated.