Originally Posted by edlank
Out of the circuit, the apparently overheated resistor is 440 ohms, the same as in circuit. It appears to be wire wound. It is about 1/4" diameter and 1.25" long.
The resistance of the motor is close to the value shown in the specs.
Then I'd gamble $140 and replace the circuit board, depending on how much a new fan & install is.
Here's the rationale:replace part in device or buy new device
140 >enter parts cost PC in dollars
10 >enter likelihood in percent L of having to buy a new device after you buy the part
500 >enter new device cost NDC in dollars
190 = your calc'd part replacement cost = PC + (NDC x L/100)
so choose part replacement.
This decision is a toss-up when L is an unbelievably pessimistic 72%.
Our ceiling fan blade broke off and the new fan was not exactly a drop-in replacement. I had to spend quite a bit of time in the attic making a custom support structure so you might want to factor this in.