Nothing happens when you click it; I'm assuming it must be a JS conflict but have no idea how to resolve it. Tried uninstalling any recently installed apps but that didn't help.
Eunice here from Shopify, thanks for posting!
It looks like the password protection for your store is currently enabled so I'm not able to view your storefront to test the add to cart button. However, a lot of add to cart issues are cookie related so let's dig a little deeper. Which device and browser are you using? Carts require cookies in order to work and some default cookie settings can be quite restrictive in the cookies that they allow, which can cause issues for shopping carts. I recommend checking your cookie settings, and if cookies are fully enabled and the add to cart button is still not working, then it'd point to issues elsewhere which we'd need to investigate. While we're not able to provide account-specific support in the Community at this time, we'd be happy to help via callback, chat, or email via the Shopify Help Center.