GE Monogram Won't Drain completely

My dish washer won't drain completely. It's a GE Monogram from 2006 or 2007. (It came with a new house). The water level does not seem to rise when my husband runs it to try to see if anything has changed. But there's a 4 inch puddle of whitish water in the bottom basin that did not get any lower after leaving the dishwasher like that for several hours today.

We felt around the drain with our hands and did not feel anything obviously clogging the drain. We ran the garbage disposal in the sink to make sure that's not the problem. Any thoughts?