There are a few things you can try, apologies if the post is long.
Double check your TV to see you are using the correct source input for the 360 box.
Have you tried removing the HDMI cable and plugging it in again to a different HDMI port, then select the new source using your TV remote?
If that fails disconnect the 360 from the mains for a couple of minutes then plug it in again and see if it reboots to a screen you can see. If that doesn't work disconnect all HDMI leads from your TV except the 360, then unplug the 360 from mains and try again
Do you use the TVGO app with your 360? If so open it and in the settings click on Live TV then do the following using the TVGO app. There should be 3 icons in the top left of the screen, click on the middle one, and on the screen that opens click on the remote control icon. On the next screen click on the Menu (Home) icon - even though you can't see it this opens the menu's on the 360. Press left twice then down once, the right twice and click on OK. This opens the HDMI resolution page. Press down 3 times and click OK, wait 2 or 3 seconds and press OK again (this sets the resolution to 1080i) then click menu 2 or 3 times and hopefully you will have an image on your TV again. You may have to press the back key on your 360 remote.
You can also do the above blindly using your 360 remote.
You can also try the following blindly using your 360 remote, or using the TVGO app. Press the Home button, then left twice and click OK Press Right twice, then down 7 times and press OK Enter your pin number (should be 0000 unless you changed it) press OK then up once and press OK again. The box should then restart (it will be performing a factory reset but keeping all your recordings and series links)
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