Thanks everyone for the ideas.
First, no, there is no remote with this vehicle. No door locks, no alarm, nothing like that.
I have had the car several years, and never haf the problem before. It not only cranked the engine but quickly started. The key was not in start or crank position, so it could be freely removed. I moved the key back to start position while the engine was running, then back to stop. It stopped momentarily, turned over and started again. It did the same thing when I removed the key. Finally in stop position after about five tries, the lights on the dash went out, I gingerly removed the key, and it did not start again.
I left the car for about three hours, and it did not start itself.
I then removed the negative battery cable which I have not yet connected again (out of town for a few days, so I did not want "Christine" leaving me-- I still love her).
I am hoping this may reset the electronic start functions. The cat is not driven often, so I will take the advice of one of you and fully chargd the battery (though I do not think it was low).
I am in Puerto Rico in a remote mountain area, so access to a GM dealer is not easy.
To-morrow I will reconnect and charge the battery, and make some starting on and off attempts to see what happens. I will report what happens.
I see some of you say the key with the chip when not present will not allow the engine to run. How then did the engine continue to run with the key withdrawn from ignition?
Thanks everyone, and I hope the GM man will stay with me to help resolve the problem!