Servicaixa send an email confirmation.
The subject starts with.
ServiCaixa - Confirmación compra entradas para General Diurna
The email is very clear and you will know if you have received it.
Maybe you gave the wrong email address by doing a typo.
Look in your spam folder.
Search all your mail for the word ServiCaixa.
If you are not successful try phoning them and they will be able to sort it out.
902 888 001 / 934 923 750 from Spain or +34 934 923 750 from outside Spain.
There is more info about buying tickets herehttp://www.granadainfo.com/ticketsalhambra.htm
Secure websites start with https
(note the S)
It is unlikely that servicaixa would ask for credit card details not using https
A padlock should appear.
If the date on your computer is wrong it may make the security certificate look out of date.
Internet explorer used to falsely acuse our site of being insecure when it was secure.
Try firefox or chrome.