Here is the culprit to my water damage problem - a very disintegrating old galvanized pipe.
It wasn't the dishwasher connection as originally thought. Heck, that would have been easier to fix, so of course it wasn't going to be that.
So, after new floor joists, new studs, all new plumbing - no water access for three days - and a few kitchen cabinets taken apart - all should be well by Friday. And by Friday, I should be able to use my fancy new dishwasher.
Living in a 61 year old house certainly has its perks, doesn't it. Just for the record, Universe, I could use a break now.