Amazingly enough, the robot panned out for me. I got a phone call from the AT&T tech shortly after noon. He rooted around at the neighborhood junction box and concluded that something was fubar on their end. Half an hour later, he showed up at our house to make sure he'd gotten it all fixed. (He had.)
I wasn't 100% clear about his explanation of the problem (something to do with my wire having gone bad, and needing to replace the DSL card, but he had to try three DSL cards to get one that actually worked), but everything's now working like a charm.
Amusement: after Hurricane Ike, I've been nervous about my above-ground telephone and cable tv wires, which go through our backyards. One of the neighbors has an old oak tree with a fairly significant branch (maybe 1 foot in diameter) resting significantly across the cable and phone wires. I don't know the people who own the tree, but I know their neighbor, who mentioned that they do love their trees dearly. Well, that old tree is threatening to take out phone and tv for the entire block.
While I had the AT&T dude at home, I walked him out back and showed him the tree. "Boy, that's sure putting a lot of tension on the line," he said. He said he's run it by his supervisor and they'd sort out whether they wanted to come out and deal with it. I mentioned that the owner really loves his trees and he replied that he's been in situations like that before. He just calls his supervisor, they get the police out, and then they get back to trimming the trees. It's pretty straightforward -- any tree that gets in the right-of-way can be trimmed or cut or whatever.