Greetings Peggy,
Sorry to hear you've been having an issue connecting the Surface to your LG TV. From what you've noted, you are getting video correct?
If so, would it be possible for you to take a picture of the LG Icon showing up, along with the System Info screen of your TV?
I'm looking into the HDMI issue and trying to get as much info as possible.
This is the same problem I had.
This is the screenshot when attached to the display (as you can see, the second display shows up, but the device isn't listed in playback).
This is the screenshot when I unplug the display - only now does it appear as a playback device, but it's (obviously) listed as unplugged and therefore can't be 'set as default' as so many people are prone to recommend.
What do you mean by "system info of your TV"?