Hello and welcome to Just Answer. My name is ***** ***** I will be happy to assist you with your electrical question.
1) Did you purchase a generic 3 speed fan replacement switch from Home Depot or Lowe's or did you purchase an "identical" replacement switch for your particular fan model? If you purchased a generic switch replacement, there is a good chance that the switch may not work. Even though the switch may look similar on the outside, there are a variety of fan pull chain switches that have different internal switching patterns. Thus the reason why an "identical" replacement switch must be purchased.
2) Most, but not all 3 speed ceiling fan switches require a total of 4 wires.......ie.........3 wires for the different speeds and 1 wire for the hot wire (power). Somewhere, you maybe missing 1 wire?
3) Do you have an AC voltmeter to confirm which wire is the hot wire? Usually, it is the black wire for most fans and the black wire normally connects to the "L" (LINE) position on the switch.
4) If you did not label or take a picture of the wire colors on the original switch, it will now be a method of trial & error to connect the wires assuming that the switch will work with your fan model.
For whatever reason, ceiling fan manufacturers never provide a wiring diagram on the internal component wiring and a diagram is never available.
Reply back to me on the switch replacement and if you are able to locate a 4th wire.........Thanks............Kevin:)