Cadillac 1998 STS has trouble starting???

A month ago I had the car towed to shop because Cad. wouldn't start. It get to shop and then starts , no problem. They check for other problems and finally say its the battery.
Put new battery in and car is O.K. for about a week. Now it is acting up and refuses to start on first try. It will take maybe 10 times turning key and finally starts????? It is happening more frenquently now.. Is it now the starter or is it the ignition. We are getting afraid to drive the car and then have it not start once its turned off. New battery and there work was $300.
Any help ?????? or suggestions??????\
Thanks Terry
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wrote:

I had this problem with a 2001 DeVille. The problem was in the ignition switch itself, which had to be replaced.
Best,
Bob
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