Here are the zipped up files in anyone is interested in this problem.
Edit: So I was messing around with this program some more today and realized that my data is getting passed to the main GUI. It's just that the data does not get updated in Backprop_GUI_OpeningFcn. It only shows data = []. I typed in handles.data in the weight_slider_val_Callback and I get the data values if I move the slider. Question is this, why can't I see these values in the Backprop_GUI_OpeningFcn? This handle problem ties in with the weight_slider_val handle because if I comment call to @mouse_over, I can operate the slider with no problem.