OK, here goes.
DirecTV carries all local channels, except the 4 major networks in NY and LA on spot beams that can only be received in (or near) the actual local market. Apparently the ones for your market are on one of the side sats, and you can only "see" the main sat.
The four majors (NBC, CBS, Fox, and ABC) from NY and LA and distributed nationally, but only for people who live in "white areas" (places so far from town they cannot get TV with a normal antenna and in one of the 8% of markets where DirecTV does not carry the local stations) and truckers, RVs, boats and other such. Or if you happen to (or claim to) live in the NY or LA metro area. You have claimed to live in NY, and thus get "your" big 4 locals. However all of the other stations in NYC, including the CW, are on a spot beam and you are 1000 miles outside the spot.
However the CW is different. DirecTV also has a CW local for the, actually quite large, area, but its from Washington, DC. It get delivered to those whose local station package does not include a CW station (lots of smaller towns do not have a CW affiliate) and to the others I described above. Since you "live" in NYC, a town that has a CW affiliate, you cannot get the substitue national feed. Customer Service cannot help you.
You might want to consider seeing if you can place another dish somewhere where you could see the other sat, which can be hooked up to make the box think it is hooked up to a proper 3 LNB dish.