No refund store but gave a damaged item
I ordered an eyeshadow palette online together with other make up tools but when I received it, the palette's mirror has a crack and some of the eyeshadows were crushed. Not only that they are not answering my messages but also the store has a no refund policy. I cannot give the palette to the person that is supposed to be receiving it because it was damaged.
Since the store is not giving any refund although it was their fault, you can report it to the local trading standards department because it was part of a statutory right of a customer. You can send them an email and notify the shop about what you are about to do. That way, maybe they will do something about your ordered products.