Ok, your button is on Analogue Input #10.
The cascading effect is normal and a GOOD sign. There is really one 1 analogue input on the FB, and then it switches really really fast between all the inputs and reads them. This is common practice. THe problem is when the pin is floating again, you have nowhere for that excess charge on the sample/hold cap to go. So it just sits there and slowly degrades. Until it samples Analogue #10 again and it recharges it all the back up. If you put a jumper to ground on Analogue Input #1, that should make it easier for you to visualize.
Perfect! Then it is working. The way I described was it is high when not pressed, low when pressed. This seems to be what you are getting.I'm now back to reading 0 when the button is pushed... Bahhh..
Huzzah, a single button works.
Now you can read up on voltage dividers (wikipedia has a good article).
Size R1 and R2a-R2d so that they make different voltages when connected.