Maybe your fan motor is connected in series with another circuit, rather than in parallel.
I think that you are correct about it not being the cap, unless they had a bad batch of caps.
I would measure the voltage at the fan motor an see if it is getting 120V.
I would think that if the fan had lights also, then they would be dim also.
I have also seen bad light switches, that arc inside, but you can normally hear them arcing. (making bad connection)
Good Luck with your project
Have a Great day.