Neural Network outputing the same value / normalization
If it works for your data, I would suggest normalization by:
input = (input-median(input)) / std(input)

Also try to use a smaller batch size for initial training. And triple check how your data actually looks like. The same goes for the labels.

Depending on the framework, you should also check the data type of the labels. Some unfortunate computation might cast your float probabilities to int, thereby killing any meaningful output.

I can recommend Andrew Ng's famous Coursera lectures. They give good insight into what happens within the neurons.