Take the TV SET adapter down to RADIO SHACK and match up a 12VDC PLUG. Then you can connect the plug to 12VDC and plug into your TV SET... Be sure you wire the correct polarity... Should Work just fine... I would fuse this new cable connector adapter probably with a 5-6AMP in-line fuse... Your TV is probably rated around 50WATTS
Will end up looking something like this...

I am not a fan of using 12VDC cigarette lighter plugs as they will get hot on you due to the poor workmanship of the cheap sockets and plugs especially if you are drawing more than 5AMPs Dc current...
They are what they are hehe...
If it were me I would setup a 300-400WATT PURE SINE WAVE INVERTER system that produces a sine wave 120VAC . Then you can plug in your HDTV, DVD player, cell phone charger, computer charger, small lamp , fan, maybe a lap blanket, etc... There is going to be much more to use for your home entertainment than just the one 12VDC HDTV set. I actually have a 600WATT AIMS PSW Inverter setup with a 120VAC drop cord to the Home Enetrtainment area and a second 120VAC Drop Cord to the bedroom area. We normally run this around 250-300WATTS for all the 120VAC things we like to have going when camping off the power grid.
It is much better for us to plug-in our low wattage 120VAC items we want to use.
Roy Ken