OhhWell wrote:
The wireless is a great suggestion. Hdmi to Ethernet then back is the best bet if you will be running the wires
However:
Depending on your budget, converting from HDMI to SDI on one end then back from SDI to HDMI on the other. With BNC to F adapters, you can run the SDI signal over the existing coax. SDI is a full digital HD signal with embedded audio.
http://www.blackmagicdesign.com/products/miniconverters
Did you look at the price on those? The cheapest is $295 and it looks like you need two of them, one to convert to analog and one to convert back. Doesn't sound like a reasonable option for what the OP is trying to accomplish.