Laptops were not "officially" allowed, but as long as you stored it properly and locked it up in your room while you were in class, then no problem. I would say about 2/3 of the people in my company brought a laptop. It saved them money on the weekends and provided something to do on the weeknights, which can be very boring if you don't need to study. I read about 12 books while I was at NSI. That was double the amount of books I had read over the last 5 years.
You really don't have enough room in your standing locker to put a TV. Once you get all of your new uniforms it will be very hard to find a place to put it. Also, you will have to carry it over 1/2 mile to your barracks from where you are allowed to park your car. I would recommend not bringing one. Laptops are easy to ignore, but TVs are a little different. On the other hand, people brought their guitars and played in their rooms every now and then. Its your call. Maybe bring one and keep it in your car if you really, really need one.
There is no cable/Internet connection in the King Hall rooms. There are several computer labs in King Hall that grant you limited Internet access (think NMCI). These labs are for you to use in order to complete about 20 NKO courses that are required within the first 3 weeks of reporting. The "E" club or whatever it was called, has about 6 computers you can use for free. There is also an Internet cafe down the road from the club. It has about 20 computers and offers free Wi-Fi. You won't be able to use either of these until about week 3 though, and then, only on the weekend. One guy did get Internet access for his laptop via an AT&T broadband card. King Hall is old, big, and makes for crappy cellphone/Internet reception. He had to take his laptop to certain corners of the building to get a strong enough signal. I could talk reasonably well with my cellphone (AT&T) as long as I stayed next to my room window.