So what you are wanting to do is play streaming movies on a laptop and use the TV as the monitor to view them. (streaming movies = watching them from the internet)
At present are you able to successfully watch streaming movies on your desktop pc? because it is the speed of your Internet Connection that is just as important.
You do not need another router, you can only have one router connected to your ISP (broadband provider).
You can connect as many pc's and laptops to the router as you wish. Routers usually have sockets for 4 cable connections to computers and then you can wirelessly connect other devices like laptops as well. Your ISP (broadband provider) does not care how many are connected, but remember they will have to share the bandwidth between them. As a rough guide, if your actual download speed is 8Mb and you connect 4 devices then each device will only be able to download at a speed of 2Mb (actual download speed = do a speedtest at http://www.speedtest.net/ to find out)
You will have to look at the manual for your TV to find out if it can be used as a monitor for a pc and see what connection sockets it has for a computer to be plugged in.