MacBook Pro won't 'blink' with new HDMI cable

The TV screen was flickering when we connected the comptuer, so we got a new HDMI cable. The new one has the built-in adapter for my MacBook Pro Mini DisplayPort, so it's all-in-one. Now, for some reason, when I click on "detect display", nothing happens. No blue screen, no 'blink', nothing. The TV isn't connected to the computer. So I go back to my my old HDMI cable. Lo and behold, my MacBook detects it. Then, on a whim, I plug in the new cable. Now it works. Beautifully. But when we turn on the TV and computer from scratch, nothing. In other words, the computer detects the old cable at start-up, but not the new cable. However, once an HDMI link has been established with the old, faulty cable, I can switch in the new cable and we're good as gold. Obviously this is not an ideal situation. I'd just like to plug in the new cable, hit 'detect displays', and be up and running. Why won't that work? Thanks for the help.