Hmm the fact that a computer output with a 1080P signal does work would suggest a settings related issue with the camera. I did recently speak to another customer who mentioned having issues with their HDMI output on their gf50 camera. They mentioned needing to change their default FPS setting to 59.97 or 30 FPS in order for the camera to output a signal. Perhaps this might help or resolve the issue?
Unfortunately we do not have a gf50 camera to test with so we are limited on the camera support we can provide in this instance.