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Hello, Do you have another source you can connect to the Sony using HDMI so we can confirm the issue is in fact the TV and not your Tivo box? HDMI generally either works, or it doesn't so since you've tried other cables it would make sense to try another device (such as a Blu Ray player, etc.).
Are you still with me here? I'm asking for the above to be performed as a basic TEST. Let me know.