For the video, you just connect the Joey's HDMI output to the PC monitor, as long as it has an HDMI input. You would use an HDMI to DVI adapter, if it only has a DVI input. If you only have an ancient analog-only VGA input, you will need an HDMI-VGA digital-to-analog converter. Monoprice has them for around $30.
For the program data, connect the Joey's ethernet port to your LAN's router or switch. I assume there is a wired port somewhere in your office room. As long as your Hopper is connected to your LAN, they will link to each other thru your LAN, no coax required.