Thought I will share my experience with Renfe website. Hope it helps others (mostly in America, because of credit card decline)
The best prices for AVE fast trains are through the Renfe site. There is a $15/$20 markup per ticket in other places. Specially, if you are buying for family, it adds up.
The credit card didn't go through even after calling the credit card company multiple times. They even unblocked the transaction.
What finally worked was a paypal account. It first declined the paypal transaction. When I called the paypal they said they declined it because they didn't know what site it was. So I had to answer couple security questions and then tired to buy the tickets again. It finally went through.
So buy with paypal but let them know that you are making a transaction through Renfe.
Hope it helps!