Just hook it up via HDMI and select the appropriate HDMI channel as your source and ignore the "PC" hook up. Some TVs will allow you to change the name of each hook up but it doesn't really matter what you call it.
You might have to disconnect the HP monitor to get video on your TV though. I'm not 100% positive but I don't think HDCP likes dual output since it can be a copy protection issue. Try completely unplugging the monitor and see if you can get video to the HDMI on the TV.