Sorry to hear about your display.
The reason you're only seeing a ROG logo is (most likely) because you've set the screen mode to TwinView or Tablet mode. You're not getting any further than that with the desktop dock I'm afraid, since you need to get past the lock screen to change that.
You might be able to fix your problems by getting hold of an HDMI to USB-C cable. That setup will default to mirror mode, making it possible to see your screen on the TV. This assumes your touch is still working of course.