The custom node template file is not working I've created template file named node--product-display.tpl.php as suggested by the Theme developer module, but the changes I made to this file don't show up.
I've also copied the node.tpl.php file in my templates directory. The changes in the latter one show up but that in the former one doesn't.

Do you have any suggestion?

I have cleared the cache. The template file is for a "Product Display" content type, whose machine name is "product_display."
Try node--product_display.tpl.php.

If your file is empty, it will show the default template file; make sure you have write something in your custom file.

Be sure to clear the cache.