I went to the Alhambra in 2019, so I have no current experience with its ticketing website. I also have no particular expertise in this area.
These are the things I'd try in your situation:
- Use PayPal if it is an option
- Try every credit card you own
- Try every debit card you own
You can also call your credit card company and ask whether it is seeing an attempted purchase transaction. Many European websites seem to expect security features not necessarily part of US credit cards. Ask your credit-card company whether it can turn on two-factor authorization.
If none of those payment options work, I suppose it would be worth switching browsers, which can help when websites are not performing right (though I suspect that is not your issue). If no browser works, you can try switching devices (PC/tablet/smartphone).