HDMI No Signal

It's not a switch. It's a HDMI Repeater which routes the signals via processors and outputs the signals to the HDMI output. There is no direct passthrough, without processing the data first and adding a delay in signal.

You have shown no proof in the HDMI signals being directly passed through without being processed and your assumption on 50-133ms of Xbox 360 processing delay on Campaigns is Ludicrous too...

No. It functions via HDMI in, if you're not feeding a signal via the HDMI in then there is nothing to view. I imagine converters for a bunch of tv signal styles are in the works though.

Reset the console display settings

If the display problem is still not resolved, reset the display settings of your console. Here’s how:

1. Remove any discs from the disc tray.
2. Turn off the console.
3. Turn on the console.
   Note If you are using an Xbox 360 Wireless Controller, turn on the console by using the Guide button on the controller. Make sure that you use the player 1 controller when you do this. The player 1 controller will have the upper-left light illuminated.
   
4. As the console starts, on the controller, press and hold Y while pulling the right trigger. The display settings are reset to the default settings, and then the console automatically restarts.
   
   Once the display settings have been reset, consult the documentation for your TV to see what resolutions it supports with your video cable type.
   
   Let us know how you get on.

Perhaps switching to component cables until you resolve the issue would be a suitable option for now, there is not much defference between the to cables on a 26" screen, i actually use a component cable on my 250 gig slim with a 40" TV and the picture is
still great...

Hi. I bought this cable

RUIPRO HDMI Fiber Cable 40 feet Light High Speed Support 18.2 Gbps 4K at 60Hz HDMI 2.0 Subsampling 4:4:4/4:2:2/4:2:0 Slim and Flexible With Optic Technology 12mt.

Now it works perfect