For the longest time my 2-year-old daughter, Ava would not play independently. If she played with her toys she needed mommy or daddy to sit with to her or join in. The only toys she seemed to pay attention to were those that she could hug and sleep with.
The move to playing independently seemed to happen overnight for Ava. While I was rearranging her toy box one day she became memorized by all the toys she had never bothered to look at by herself. She happily played alone and from then out she has been using her imagination!