This customization applies to Parallax 3.0+. For information about updating your theme check out this article.
If you would like to completely disable the side-cart/sliding-cart/drawer from appearing when the cart button is clicked (so that the link will direct to the cart page instead), go to Admin > Online Store > Themes > Actions > Edit Code > header.liquid.
Locate this code (around line 28):
<a href="#cart" class="icon-cart cart-button right"><span>{{ cart.item_count }}</span></a>
... and replace it with this code:
<a href="/cart" class="icon-cart cart-button right"><span>{{ cart.item_count }}</span></a>
Then locate this code (around line 237):
<a href="#cart" class="icon-cart cart-button"><span>{{ cart.item_count }}</span></a>
... and replace it with this code:
<a href="/cart" class="icon-cart cart-button"><span>{{ cart.item_count }}</span></a>
The cart button will now link directly to the Cart page.