Had almost the same thing happen on mine last year. Pod still sitting in the cup half dissolved, dishes coming out crusty. Before you decide repair or replace, try this stuff becasue most of the time it's not actually the machine dying. First, run the kitchen tap until the water's hot before starting the cycle. Pods need hot water to break down and if the machine fills with lukewarm water at the start, the pod just sits there. Second, open the dispenser and work the door by hand. If it feels stiff or doesn't spring back, the latch might be gunked up with old detergent. Scrub it out with warm water and an old toothbrush. Third, check your spray arm for clogged holes, especally the one under the dispenser, since blocked jets means water never reaches the cup.
As a test, skip the dispenser entirely and just toss a pod in the bottom of the tub. If it dissolves fine that way, your dispenser is the issue, and on a ten year old machine that's usually a cheap fix or even just cleaning. If the pod still doesn't dissolve, then you're looking at a heating or circulation problem and that's when a tech or a new unit makes more sense.