2001 Cadillac Deville 2001 Deville Won't start sometimes

I have a 2001 Cadillac Deville That sometimes will not start. When it first did this I had the battery replaced thinking that was the problem but it wasn't. It still does it. Most of the time it starts fine, sometimes it just does nothing when I turn the key. The dash lights up, and I hear the fuel pump. I will keep turning the key a number of times and then it will start. Sometimes it takes more tries than others. I took it to the dealer and of course when they had the car it started for them everytime. So they couldn't help me. Please help! I am tired of worrying everytime I get in my car whether it will start or not. Thanks!