Have you tried cleaning the lens yet? I had an old DVD player that rejected most discs that started working again after I cleaned the lens. You can get a cheap lens cleaning kit from any major appliance store or even Amazon (like this one-https://www.amazon.com/Endust-262000-Lens-Cleaner/dp/B003EEMDMC/ref=sr_1_1?ie=UTF8...-1&keywords=dvd+lens+cleaning+kit).
My XBOX 360 E does that if I'm on the wrong channel. Did you double check your input selection on your TV? Have you tried plugging it into a different device (i.e. a monitor or another TV)? If it still doesn't work with a different display device, then there seems to be a problem with the XBOX's video card recognizing that you're connected to a display device. Did you try the component cables that came with the XBOX in your TV? If it works with the component cables, then it is just a problem with only the HDMI port on your XBOX, not the entire video card. If it is the display adapter, then you'll need to replace the whole motherboard, since it's integrated. At that point, you'd probably be better off with buying a new 360 or a One. There's a repair guide for the 360 E here that you'll need to use to replace the motherboard if you chose to go that route. Hope this helps!