Hi Squeak,
No, this isn't the dealer. They called me before doing any extra work, and they showed me all the problems. This work all needed to be done.
It's now in the hands of a mechanic who worked for GM for 7 years, and specializes in electrical problems. He told me he is very familiar with this problem and that it is in the communications between the fuse center and various modules. He said it may take a day or two to trace the actual problem, either a wire, connection or module, but he is 100% certain he can repair it. We'll see!

The Taurus is a 99. It was my mother's and was driven very little until a couple of years ago when she quit driving and I bought it. It had only 9,000 miles in four years.
Anyway, they replaced the battery and a relay and said it is fixed. I drove it yesterday evening and this morning and so far seems to be o.k. I still think there is something pulling the battery down, but haven't had time to check it yet.
Thanks for they help!
DonM