A:Answer I don't know your specific hook-up or situation, but I would think it would be one of 3 problems.
1 - The new TV is defective. 2 - the cable box (assuming you use one) is defective. 3 - The cable box to TV cable (assuming HDMI) is defective. I would suggest troubleshooting in this order: 1 - swap out the cable. If it works, the cable was bad. If it still doesn't work, the cable's not the problem. 2 - Swap out the TV. Surely you have another TV in another room you can hook up temporarily. If it still doesn't work, the cable box is bad. If it works the new TV must be defective.
By now you should know where the problem is, but to confirm hook the new TV up in another room. If it doesn't work, you've confirmed a defective TV. If it works, you've confirmed it is a bad cable box. Kind of a pain in the neck, but you should find where the problem is and take the needed action - return the TV as defective or call the cable company about the box.
By the way, this happened to me, but I lost the sound, not the picture. I thought my new TV was defective but I did my own troubleshooting as above and I found out the cable box was defective and they replaced it - problem solved.