I am wondering about a house with long coax runs. There is one control-room, where all the coax terminates, and from where the coax runs to many rooms in the house.

Currently we have an ancient (SD) DirecTV receiver whose signal is split and sent to maybe 3 rooms in the house.

We want to upgrade to an HD DirecTV receiver, but I believe that HD DirecTV receivers use analog component video and HDMI cables.

Is there any way to continue to use the coax cables in the house to send HD satellite TV signal to HDTVs distributed throughout the house? To clarify, is there a way to convert the signal from component video (or maybe HDMI, despite DRM issues?) to coax and send over our existing cable infrastructure?

Thanks!

Negative, coax cables do not have enough bandwidth to send and HD signal through.
Standart Def only. The receiver is locked to output only 480i through the coax connector.

You either can
1) run component/hdmi cables to each room (everyone watching the same channel)
2) buy 2 more hd cable boxes and place them in the 2 other rooms (can watch different channels)