A fairly common request is to hide the add to cart functionality for those products whose price is zero ($0)

You will have to edit either your Templates/product.liquid file or Sections/product.liquid file (ShowTime 5.x). 

Please log into your store as an administrator and edit your style.css.liquid file. To access the file, please follow these steps:
  • From your Shopify dashboard, click Online Store > Themes and look for ShowTime.
  • Click the ... button and choose Edit HTML / CSS from the drop-down menu.
  • Navigate to the Template or Sections folder and locate the file called product.liquid.
  • Click on it to open the file in the editor.
  • Please back up this file to a text file prior to making any changes.
  • Search for 
    {% if section.settings.show_product_cart_postion == "top" %}
  • Replace it with 
    {% if section.settings.show_product_cart_postion == "top" and product.price > 0 %}
  • Repeat for 
    if section.settings.show_product_cart_postion == "bottom"
  • Click the "Save" button to save your changes:
Code excerpt

The code will result in the following display.

Product with a price of $0

Product with a price > $0