Did you also already register with PayPal to upgrade your PayPal account to PayPal Payments Pro and have that registration approved at their end? If so, is your PayPal Email setting in Seller Admin > Edit Profile an email address linked to the PayPal account you upgraded to Pro, and is that the PayPal account where you'd set up the API access?
Simply setting up our API access permissions (Step 4 in our instructions) would not work if your PayPal account had not already been upgraded to Pro at their end (Step 3). At present, it appears new registrations for PayPal Payments Pro are only available to sellers based in the US, so if your PayPal account is not registered as a US-based account, you would not be able to use PayPal Payments Pro.
Bear in mind that even if you just use PayPal Payments Standard, PayPal's checkout site can usually offer buyers a card-based payment option if they don't have a PayPal account -- see this help page for further details and recommended settings: