This error occurs because the node config-> global-> crypt-> key-> in app/etc/local.xml was modified or deleted after the activation key was saved. In order to resolve this problem, you need to remove the key from your database using the following SQL query:
DELETE FROM TBLPREFIX_core_config_data WHERE path LIKE 'gomage_activation/slider%'
Where ‘TBLPREFIX_’ is your DB tables prefix for Magento®.
Then go back to the activation page and activate the extension.