You don't need a projector if you can cable your laptop to the TV with a long D-Sub or HDMI cable. See what sockets you have on the back of the TV set.
Depending on where you live, you should be able to find a website which shows some TV channels - in the UK it's TVCatchup at http://old.tvcatchup.com/register/ and you may even find it works in your country. I get 40 channels in Britain, maybe not the best ones but a decent choice for a free service. You have to suffer a thirty second advert before you get to choose or change channels.