I don't own a Marantz, but rather a Yamaha RX-V863. I had the exact reverse of your problem. I can hear sound, but no picture. In my case, it was the cheap HDMI cable I was using. Do you have any other devices that use HDMI? Maybe an upscaling DVD player or PS3? Perhaps you can test using that particular HDMI port with other devices, with the same HDMI cable.

So you can get sound from your TV speakers? I was thinking it might be related to the dashboard update fiasco some time ago. There were complaints that certain users who connect using HDMI found out that they can no longer get sound output via HDMI. But since you can get sound from the TV, it's not the 360 issue then. When connected to the Marantz, is it just the 360 having no sound? What about other devices (if any)?