Once they determined it might be "in the lines", they gave me a tracking number for the service call, and said they'd send a "line tech" out by at least 6pm today.
He showed up about an hour ago, tested the DSL signal out on the box outside my house...nothing! He then left, said he needed to go to the big box thing the phone company has up at the start of this road. When he came back, he said whoever was at the box yesterday fixing my phone problem had neglected to reconnect the DSL portion. He hooked the electronic thing he had with him back up to my outside box, said he was now getting "sync". I came inside, turned on the PC, managed to get connected finally.
The repair guy said that happens often, that one division of BellSouth will fail to give another division all the important information about a persons account, and that the phone repair guy yesterday probably didn't realize I was also a DSL customer. Anyway, for the meantime, things seem to be functioning. Still, I contacted the Louisiana Public Service Commission this morning, and registered a complaint about BellSouth.
I'm assuming I'll get some "credit" for the downtime on my phone/DSL bill this next time. They gave me an $8.13 credit for the telephone downtime from last month.