How to show/render 'Add to Cart' button?
There are a couple of things I would try to see what is going on.In the post that you referenced, they said the following code. render($content['field_product']).

Have you tried just rendering the whole content using the following render($content), which for you I think would be render($productw). This should render the whole product including the add to cart button.  I am guessing that if it doesn't show up then, then there is something wrong with how you are getting the content and field_product isn't even available to render.

Also, which display are you affecting when you change your product reference to Add to Cart form?  Your default or your teaser? Are you modifying the right template?