Not sure how Amazon ships TVs, but I recently bought a TV on the internet and it was shipped to me by a local freight carrier. Part of the instructions I got when I purchased the TV were to unpack and plug in while the delivery driver was still in my apartment and only to sign for the package once I was satisfied there was no damage from shipping.

If your TV was just delivered by UPS/Fedex who sometimes don't require a signature nor would they wait around for you to test, I would just say it was damaged upon receipt (either shipping or from the factory). I would call Amazon immediately, I think the longer you wait the harder it will be to claim it was damaged during shipping. See what Amazon says for exchanging and if its not satisfactory, call Amex.