Remove the LCD completely, gut the laptop. You need only the mainboard. You will need to mount so the CPU fan can vent outside the TV case. You will need more active cooling as well to ensure the airspace you're restricting isn't going to damage the TV (thermal probe & simple monitoring proggy maybe? find 'coldest' area of TV and put there) You also need reliable IR usb reciever which can power up/down the laptop cleanly, wireless KB with working power options, or some laptop that has HDMI-CEC which I don't know about. You will need an SSD or way to mount drive, and probably networking abilities. You will also need to hack the TV case up to access USB/HDMI/audio/network ports, or directly wire them inside the TV. Ensure you can't connect another device to any direct-wired ports or you'll have fun. There should be no problem tapping the AC off the incoming line and wiring direct to the laptop power brick and leaving it secured in the TV, unless you have a 650W+ plasma. (most line cords will handle 125V 6A pretty easy. Most TVs are 50-300W, and most laptops are under 150W)
Its totally possible, use your head a bit though and you won't fry anything. laptop boards are very tiny these days and TVs are huge. your laptop housing would be a good template for where to put ports. For the effort required, and the huge possiblity you will have a dead TV and broken laptop - I'd get a TV mount and secure the laptop to the arm of the mount somehow, or get a small shelf to put the laptop on above/below your TV. You can remove the LCD completely if you are using HDMI out, which will half the weight & size. Unless you have a plasma laptops are super light and the added 2-5lb of a laptop won't matter on the arm.