As an aside – when you sign paperwork acknowledging delivery from a courier often the wording is "received in good condition". When this is the case I delete the "in good condition" and write "not inspected". These are contractual documents.
It's then important to report any damage to the supplier immediately and agree how deal with the issue. This gives the supplier the very best chance to investigate the cause and fix the problem. Quoting consumer protection legislation at this point is usually unhelpful, whereas an adult conversation on how to get to a satisfactory solution is usually beneficial.
A quote from a supplier donkey's years ago, who had screwed up a product delivery, which I've never forgotten – "Steve, I'm on my back, you've got your boot on my neck – maybe if you help me up I could go fix the problem?"
Steve