I'm suspecting that your TV:
Doesn't like 720p signals being sent through a VGA output, at least concerning that PC. It could be outputting something that it's not expecting for VGA for whatever reason.
Your TV taps out at 1360x768. Most 720p TVs don't have a native resolution of 1280x720. Many of them actually top out at 1360x768 or 1366x768, while some older TVs top out at 1024x768.
If it's not bothersome and 1360x768 happens to work, just use that.