If you turn your channel on your TV to channel 3, and you hook up the RF connector box to the TV, and you switch it to game, you will get a picture. If not, try Channel 4.
If you still do not get a picture, then something is wrong with the box, or the atari. Usually its the atari... the atari is prone to have the power jack snapping off at the solder joints on the inside of the atari, as well as the power brick dying.
If you plug in the power jack, and you see a spark, then your power brick is fine. You can also test it with a multimeter, the tip is hot, the back of the tip is ground. It should read 9V, 500mAH. If not, then you need a new brick.
If you are getting those readings, and it is not powering on, check to see if the jack is loose when you plug it in. If it is, then all you have to do is open the Atari, and remelt the solder joints on the power jack. You can't screw it up, the joints are HUGE. Just hold the iron on each of the 3 points, wait till you see it bubble, it'll fill in the cracks that formed. Put it together, and your Atari should work just fine.