The cost of an over the air television station will vary with the market. In Chicago couple of hundred million dollars or so is my guess, here in Des Moines maybe $30 to $50 million.
Now if you want to start a competing news network you need a cable or satellite provider who's will to gave (rent or lease) you a channel. The best bet for that I think would be Dish Network, privately owned so Charlie may be willing to commit a channel to a freedom news network - if he's shown they would get 250,000 new subscribers in the first couple of months. Remember Fox only gets 4 million regular viewers.