Because this is an old installation, I suspect a problem inside the dishwasher. However, it is possible that it is related to the drain. At first I thought this was a lot of water - 1.5" of water on the bottom of the tub. But the "cup" isn't that big so (a) it might actually be normal (where 3" was not) and (b) that could easily be from the water in the drain hose coming back into the dishwasher, as described below with a drain hose installed incorrectly.
Your dishwasher drain should be connected to either a traditional air gap or to a high hose loop.
A traditional air gap is a metal/plastic gadget, usually installed on the corner of a sink. The dishwasher drain goes up the air gap and the water has to literally go through a gap to go back down into another drain hose that goes down to the disposal or sink drain. I don't see how this could be broken and cause standing water in the dishwasher. Normally if this is broken, you have water all over the counter whenever the dishwasher is run and if it is clogged then you would have no water drain out at all.
However, if you have a high hose loop and it has fallen down, which can happen if it is not held up securely, particularly if any other work has been done under the sink, or if the dishwasher is pulled out for service, then you could have a problem of this sort. The high hose loop prevents sewage from backing up into the dishwasher by making an effectively impossible "hill" for the water to have to climb back up to get back into the dishwasher. If the drain hose does not go up above the bottom of the sink then water could easily drain back into the dishwasher at the end of the cycle and, if you have a clog (even a partial clog) in the main sink drain pipe or disposal then you could have some water from the sink come down into the dishwasher. See my answer at Draining problems in dishwasher. Is this drain setup ok? for a picture.