Usually your TV needs to be adaptable to PC's to be able to show the image. I tried doing the same with my TV/Laptop so I could stream events on big screen, but my TV wasn't adaptable. But I'm still looking into it.
Never heard of this.. this could be it tho.. I would assume if your TV had the ports it should work.. your laptop should send the output out in the standard way for any device that has those inputs to be able to read it.
Anyways, I thought of something else DP.
When you are trying to get it to work on your TV, you said you already had another monitor plugged into your laptop?
Unplug that monitor, and try the TV.. try to use the broken screen to go to your display options... and see if it has another screen there thats available for attaching. Its possible that your laptop never displayed it before, because you already had dual devices set up for your display.