You'll need to check back with your card provider, as you may find that the amount of the purchase has been debited from your available credit, even if the transaction had not been fully completed. If this is the case your card provider should be able to provide you with the authorisation code to go back to the retailer. The online store will then need to contact their merchant services to either complete the transaction or cancel it completely depending on how you want to proceed.
If you have any further difficulty with the merchant you'll need to go back to your card provider to complete an indemnity on the payment to claim a refund.