I would first disconnect the battery earth lead clean it and make sure it is a tight fit,as for the starter if you follow the battery live lead down it is attached to the end of it,if you think it's stuck put the car into second gear(IGNITION OFF)and rock the car back and forth,I doubt it is stuck as it would make a horrible noise when ti's started with a push,sounds like you have a bad connection,the cold weather brings these problems to the front.
Rich
January 2010
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