I'm assuming that the only thing that you can turn on and off via the separate switch is the garbage disposal. ANy time there is a switch involved, you can't just match up white (neutral) and black (hot) wires...you have to know where there're coming from and what they do. It sounds like you've got the switch loop in parallel with the incoming power, so that when the switch is closed to turn the garbage disposal turned on, you've shorted the hot to the neutral. In the process you may have damaged the switch, and might want to consider replacing it as the arc internal to it could deform or melt the contacts.
The hot from the DW box needs to go to the switch, then through the switch back to the hot lead of the garbage disposal, if the path of power is as you've indicated. if you don't understand this, it might be good to just draw it out. The neutrals would all be tied together, but the hot goes to the switch on one lead of a (probably) romex cable, and back through the switch.
If none of this makes sense, it may be time for a pro.