I succeeded in removing the drain pump from my dishwasher and putting a new one on.
In the process of doing so, I managed to knock the water supply line around to the extent that the solder joint at the cutoff valve came loose. A plumber is on the way, and even if the dishwasher works (which I'm EXTREMELY skeptical of) we have lost whatever savings we realized by making it a DIY project (and then some).