I eliminated the template for the checkout page altogether to avoid any possible conflict but it is still not connecting to PayPal. The only difference is that the Loader does show (which looks great by the way).
Could you have a second look please?
---- Addition to the post:
We just noticed the same happens sometimes when you try to checkout using credit cards. The loader starts after clicking continue but it does not seem to stop. Once I interrupt the page loading by simply reload the page in the browser and do it again - it works for the credit card checkout but not for the PayPal checkout.