I really hate troubleshooting problems with HDMI. Much of the time, there's nothing you can do because it's a hardware compatibility issue. This shouldn't be happening so many years into the existence of the HDMI standard.
We never had such problems with RCA/SCART and component video. It just sort of worked, and on the rare occasion that it didn't, you wouldn't be left staring at a blank screen. It would usually just look sort of fuzzy.