Wiring a light swith with power coming from multiple lights

Hi Everyone,

I searched everywhere and haven't found a solution. Let me explain. my basement has a light switch at the top of the stairs that turns on a light at the bottom of the stairs. that light then power a separate room with 2 banks of high hats. if the basement light at the bottom of the stairs is not on, the other lights won't work. I'm trying to add a light at the top of the stairs since the stairwell is so dark. when I popped the cover, I saw just a black and white coming into the switch. because of this, I assumed the lights are being fed power and the switch is the end of the line. so I wired the scone as follows: white of the scone to the neutral coming into the switch (before the switch, of course). the black of the scone connected to the switch. the black (hot) connected to a separate wire (white with black tape on it) running to the switch. I was sure this would work, but when I put the power back on, the sconce worked, but the lights down in the basement didn't. I tried to figure out how things were wired in the basement, but it's near impossible to follow the trail. being that there were only a black and white coming into the switch, I can't imagine it's anything but power coming in, not going out. I also tested the switch with a volt meter and the black was only hot when the switch was on. I'm not well versed on electrical code or theory, but I would think that the black would always be hot and the switch would be what closed the circuit, so I'm even more confused. Any help would be great. I've called 3 electricians for general work in the house and figured to have them deal with this, but not a one has returned my calls. it's impossible to get these guys to call back! Thanks in advance