Thank you SHORob and tempfixit.
When I try to restart there is clearly spark. The started engages and it revs to about 2000 rpm and then it is like a switch is turned and the engine shuts down. This whole thing takes maybe 3 seconds. I can then do it again ... and again ... and again, but it won't stay running.
This is a SES model. I don't know what to say about the engine type.
There is the standard Taurus security. Then there is an added KARR security. I called KARR and they said that it wasn't them because their system won't let the started activate.
Let's keep talking. There has got to be an answer here.