You need a tuner, not a demodulator.
As you found out a bit too late, monitors are TVs without tuners and possibly sound systems.
Where do you want to get the television programs from?
If you expect to use cable TV as the source, the cable box is it. You're home.
If you want to get OTA (over the air) TV, which is free, you'll have to purchase a standalone TV tuner and most likely invest in a decent antenna. Be aware, though, that not all TV tuners are Hi Def. They cost a bit more than standard ones. Be careful there.
Purchasing a TV with a built in tuner would have been much, much cheaper. That inexpensive monitor purchase will cost you more money than you saved. But, looking on the bright side, most monitors don't include sound systems. You lucked out there.