Replacing Kitchen Lights

I need some electrical help: I am replacing the lights in my kitchen...I removed the lights 6 weeks ago to rid the ceiling of popcorn and I had just bought the house. On Sunday when I went to put up the new light fixture, as shown in the pics, I found that this one box has lots of wires...2 sets of 3 wires wrapped together, including both whites and blacks on each set. When I took the old fixture down, I didnt pay attention which side the black wire and the white wire from the fixture was attached to on the box.

I was told all these wires are because they are running wires to a second circuit (right terminology?) to be controlled by the same switch.

I have 3 lights in the kitchen - This one pictured, a second one over the sink - which has it's own switch for and I could see some wires wrapped together stuffed up in the box, and then the 3 wires hanging down to attach to (the ground, white and black). The third light is over the dining area and has only 3 wires - black, white, and ground but is controlled by the same switch panel as the main light (with all the wires).

I couldnt get any lights to work...Guess my main question right now is - does the main light box have to be properly working and connected before the other 2 lights will work?