Python Neural Network library/program with simple installation? (Solved?)
If you are trying out neural networks, I would recommend keras, it is a wrapper around TensorFlow. With just a few lines of code, you can build a neural net.

Scikit learn is really good for ml algorithms like logistic or linear regression, naive​ Bayes, svm and others. I am not sure if it is good enough for neural networks. 

I would still think, you would require some blas library.