To figure out what is wrong these are the steps,
1. Plug the Sky box into the other HDMI input to make sure that it works. If not then try the BD player on the Skybox HMDI input. If it works on the Skybox input then you have a bad HDMI input. You can buy an HDMI switcher.
2. If it doesn't work on either HDMI input then try using the Skybox HDMI cable instead of the new one. If it still doesn't work then you may have a bad BD player.
You can also connect it to a different TV to see is it works.