Steering Problem (Lack of Boost)

Recently I developed a steering problem on my `92 LS-L w/48k mi. I get a binding feel and sqeeling noise when I make a turn from full stop or take the steering wheel to a left or right extreme when parking or making a U-turn. Once the car is moving the steering is responsive, with no binding or issues at city and highway driving speeds. One local shop told me I need a new PS pump, but if that were the case wouldn't I experience a lack of steering assist at all times?