2001 Dodge Neon Power Steering Problem:?

My power steering is going out on my Neon. Last week it started making a squeaky and somewhat clunky noise when I turned sharply. I thought it was ice up in the mechanism, but we had a big thaw and the noise didn't go away. As this week progresses, I am initially without power steering for a longer and longer time. Eventually after driving for about ten minutes or more, the power steering turns on but still makes noises, and sounds like grinding when I turn. Can anyone diagnose this problem, and give me an estimate about how much work it will be and expected costs?