Connectivity went out again, and this time turning their computer on and then off again didn't do anything. And then I remembered something else I had done: I'd picked up their phone. They have DSL, and I know from my own experience with DSL that sometimes the phone line gets messed up. And lo, that worked. I wonder how many times I'm going to have to do that. There seems to be a lot of static on their line.
(And it just went out again as I was spellchecking this post. I just hope they don't come home when I go down there to fix it again. I assume they're not coming home today, and at least I have an excuse to be down there while I'm doing my laundry.)