The capacitor is OK.
You can't rely on the component tester for any accurate result.
The fault is obvious. Save your money on buying new cap.
You really need an insulation/megger tester to track down issues with fans/motors.
Also the capacitor may read ok but perhaps it's dropped it's mojo and just can't supply the goods anymore
That looks like a run capacitor, not a start capacitor. Start capacitors are much higher capacitance and are taken out of circuit once the motor is started. It's not like a room fan would need the extra torque from a start capacitor anyway. If you pull a run capacitor out of circuit, the motor should still operate albeit slower and less efficiently. The capacitor is probably fine.
Those resistance values look very high for windings in a small fan motor, they should be reading almost zero.
Disassembly time perhaps...?
These motors should have a thermal cutoff. I am guessing from the picture: testing the resistance from the input connector (black?) to the white wire should give you a small reading, if there's nothing, then probably the fuse is open.
If you can open the motor it should be easy to test and confirm that.
OP, your ohmmeter readings do not add up? Red-White should total Wht-Yel and Yel-Blue and Blue-Red.
Does this fan just hum, or need a spin to start or is it dead?
Do the copper windings pass the smell test of minute doses of magic smoke released ?
There is your thermal fuse (see red arrow) remove it to test if possible.
So, just cutting it out should solve it? (Well for test)
That looks like a run capacitor, not a start capacitor. Start capacitors are much higher capacitance and are taken out of circuit once the motor is started. It's not like a room fan would need the extra torque from a start capacitor anyway. If you pull a run capacitor out of circuit, the motor should still operate albeit slower and less efficiently. The capacitor is probably fine.
I know this is obvious, and you have probably checked this already, but does the rotor spin freely in its bearings? These small cap start motors have very little starting torque, and even stiff grease in the bearings can prevent them from starting.
I just had a similar symptoms on a similar looking motor. The original lube had gummed up, making the bearings stiff, but not seized. Flushed out the bearings with kero and lightly repacked with fresh grease, now all good.
There is your thermal fuse (see red arrow) remove it to test if possible.
So, just cutting it out should solve it? (Well for test)
Yes you can cut it out, but for test purposes, maybe you can just follow the cables attached to its leads going to the connector and then test continuity from the plug. I can not see clearly from the pictures but I think you have one black cable coming from the connector, passing through the fuse and then another black (?) Cable connecting to the capacitor's terminal, so testing between these two points should answer the question.
If you do decide to go that way, join them with a fuse that will cope with the start up and running current of 68 watts,
stand back... switch on
and don't forget to wear glasses
if you haven't got a fuse, perhaps a 70 watt light globe as a joiner. Try a 60 and 100w if no love.
You may have to do the guesswork for fuse values or globe, or both in series, I'm just guessing what I would try
Either way it's Safety First especially on a possible bin candidate
It's a thermal fuse. The body is NOT conductive. No accidental electrical contact with anything resulting from vibration or abrasion.
For trial test purpose, you can directly link the wire and taped it. The Ohms look OK.
My advice is, don't put a fuse with exposed metal.
Use a isolating transformer [not a variac] if you want. The KVA is limited.