What are you trying to hook up exactly? Do you have an HD satellite receiver? Are the only HD inputs on the TV component (red, blue, green)?
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Sorry but we need some more information.
You say your monitor is in a room with only a coax outlet. Do you mean the only cable you can get to your monitor is the coax cable from the outlet (like the monitor is mounted over the coax outlet)?
If so, you are very limited because your monitor doesn't have any digital inputs, and I don't think you can send analog HD video over a single coax cable.
There were some wireless component video transmitters/receivers available several years ago, but they were expensive, and I'm not sure the receiver would be able to fit behind your monitor.
One complicated option would be to send a digital signal over the coax cable to your monitor. This would require outputting digital HDMI from your pre/pro and satellite box into a HDMI to coax converter, into your cable and to your monitor, then to a coax to HDMI converter, then into an HDMI to component converter, and finally to your monitor. There may be a device that will do both of the final conversions (coax digital to component) but I m not sure.