My ceiling fan isn't getting the right voltage
With the ceiling fan taken out of the equation, this will likely be a bad connection or a failing switch.  The first places to check are in the wiring above the fan, and the wiring at the switch.  Try this to track down the issue:


Shutoff the power at the breaker
Remove the plate covering the switch, pull out the switch itself, and inspect the wiring
If there are two sets of wires coming into the switch, one of these is the source, and the second goes to the fan.  Pull out the wiring so that you can easily access it without anything touching.  Remove the wire nut on the neutral (white) wire.  Turn the switch to the on position.  Turn the breaker back on temporarily and test the voltage from the neutral to the hot both before and after the switch.  Turn the breaker back off before doing any other work on the wiring.  Be sure to replace the wire nut when done at the switch.
If there is only one set of wires at the switch, then the power source is above the fan.  Turn the switch to the on position and expose the wires for the neutral, the hot from the source (that goes to the switch), and the hot returning from the switch (that goes to the fan).  Make sure the wires are not touching anything else, turn the breaker on temporarily and compare the neutral to the hot voltage before and after the switch.
If the voltage from the source is low, you'll need to track this down, on the circuit.  The next easiest place to test the voltage is in the breaker panel.  After that, you're left with identifying each switch, fixture, and outlet on the circuit and testing each one until you find where the voltage drop is occurring.
If the voltage from the switch is low, then just replace that and you should be up in no time.


Note: should you be uncomfortable with any of these steps, especially working with exposed wiring or inside of the breaker panel, then please call a professional.