Start by testing for current. Do not fool with the wires on the reverse switch.
If the light kit has its own "On" and "Off" switch, then all you need to do is find the hot unswitched power wires used for the fan. The black and white wires that you refer to, may have been disconnected on the mounting side of the fan, since the installer may have felt them to be unnecessary since he was not installing a light. You simply may have to detach the fan from the ceiling and reattach the black and white wires on that side to the appropriate hot wires using wirenuts.