I had same symptoms and my problem was a bad pulley. The bad pulley created play in the belt and resulted in a squeak when turning and on start. Take a look at your serpentine belt and see if it sits centered on all pulleys. I'll bet your idler pulley is loose.

 

Belt is centered on all pulleys. The pulley is new. Symptoms started when power steering pump failed. Serpentine belt is also new.

 

Have you checked the scribe on the serpentine belt tensioner? It should be between the I and II marks and not all the way to one side.