depending on where you live, you may have OTA channels you can watch with an antenna. in the usa its now a digital signal so quality is increased. your tv should have a tuner to pick them up (if you have an antenna) but you can get a tuner if yours does not.
you should be able to connect your tv and laptop yes. netflix, hulu, a bunch of free legal streaming sites for older content, youtube are all available provided you have an internet source. you should be able to get internet without cable from a different provider or just cut the cable off your current bill.
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we havent had network television here for a 8 years or so and have not missed it one bit.
between $1 movies we can pick up at yard sales and flea markets (good stuff too), youtube, netflix, crunchyroll and swapping movies with friends and family to watch we are never bored. we can pick up OTA tv as well but choose not to watch it.
the bill is not missed and neither is paying for a service you're always channel flipping on because nothing good is playing.