Car just turns off while driving

Ok I drive a 1998 saturn sl2 with 170k miles on it. I was driving home the other night and out of nowhere my car just shut off. I finally get it home. Try to start it and it wont start. So I wait about 20 minutes and it starts. So I think its fine. I go to drive to work the next day and it just turned off on my way to work. We pulled out the spark plugs. The first one was covered in what looked like oil. And the other three were just looking super old. So I start my car. And time how long it stays on. And it only lasted 6 minutes then turned its self off again. I changed the spark plugs and the problem still continued. I noticed that there was a wire comming from the front of the engine and it was laying on there just sizzling away. So I dont know if its some sort of sensor that is just fried or what. But that still doesnt explain my problem with the spark plug. Someone please help. Thanks