Hi,
I have found that the problem is related to JCE Editor.
When I checked another editor for HikaShop (TinyMCE, CodeMirror or Non WYSIWYG) I have no problem with the "Add a product" link and the "New" product button.
For now, I use JCE for website articles and another editor for HikaShop. It works fine that way.
Later on I will try to find which plugin JCE is conflicting with and, so, generating a problem for HikaShop.
Thank you for the time spent to answer my request.
Have a good day,
Michel Gauthier