[pauldodman]

Start by finding the template product_details.tpl in customer/main in your skin folder.

Then look for the code that displays the button, e.g.
{include file="customer/buttons/add_to_cart.tpl" type="input" additional_button_class="main-button"}

Then surround that code with an if statement to determine if the price is 0.

{if $product.taxed_price ne 0}

{/if}

The button will then only show if the product has a price above 0.