If you have the new checkout page implemented you will need to manually connect it to the checkout button on your cart page by updating the checkout server behavior on your cart page, it just points to the file you choose.
It sounds like you have it working both ways. If the Express Checkout method is working for you and you have the option to check out with a PayPal account you might also be able to checkout with that method without having a PayPal account. I have been looking into this a bit and have found some more info on the availability of using Express Checkout without a PayPal account. Here is some info that I have found on the subject:
PayPal has an "Account Optional" setting in your PayPal account Profile, under Payment Receiving Preferences. Ensure that it is on.
However, note that the PayPal account optional is not available for all locations, some locations (or countries, including China) are required by PayPal to have a PayPal account before making a transaction. In this same regard, if the IP address of the buyer is determined by the system to be at a location where the PayPal account optional is not available, they will be required to create a PayPal account.
So you may be able to have the Express Checkout option setup and allow customers to make a purchase without having a PayPal account. You should start by checking for the account optional preference in your profile, then you can run a test to see if you can get this option available to you when using Express Checkout in your site. Let us know what you experience with this.