very confused on the wiring for recessed lighting
Oh, why on earth did you do that? 

Wires are not color coded for the benefit of novice installers.  They are color coded because cables only come one way: with black and white wires.   Those wires serve a wide variety of functions, but they are always black and white because cables are; they are not color coded by function unless you do this yourself with colored tape. (Which I in fact do). 

You took apart wires you did not need to take apart.  You saw a black wire from the ceiling connected to only a white wire from the ceiling: it was not connected to the ballast in any way whatsoever, yet you felt you just had to dismantle it anyway.  

I call this "trying to learn electrical by dismantling your house".  Seems pretty silly when I put it that way, but it made sense at the time, I'm sure.  

Another thing that often bites novices is the sense that the guy who did this work previously is an idiot.  Maybe, but you certainly are in no position to judge. 

Unfortunately, reversing this mistake is hard.  It may be time to call an electrician in.  

If you really, really want to press forward, then identify the two cables in this box.  Select one cable and identify the white and black from that one cable.  Connect the lamp's hot and neutral to those two wires  alone, leaving the others capped off.  If that doesn't bring it to life, try the other cable. 

In the future

Pay close attention to how things were wired before, and only touch the things you actually have to.  

In this particular case, you should be unhooking all the wires coming out of the ballast, and coiling then up and wrapping them with tape to get them out of the way, so they are out of sight and out of mind.  I don't like cutting wires on functioning ballasts. At that point, when you exclude those wires, there should 2 places that the black and white from the ballast went to. Those are the only 2 places you are concerned with, keep your schnozz out of everything else.  

Oh, and know the other thing that will save you an electrician call.   When replacing receptacles, check to see if the tabs are broken off.