I'm no expert, but my first port of call would be to use the trusty WD40.
Most cans usually come with a straw, so you can aim your squirt quite accurately.
Hopefully you'll be able to get to the spindle of the fan, about which it rotates, and get a decent squirt in, without having to dismantle it. Give the fan a quick push round with your hand and repeat once or twice more. Leave it a while (maybe overnight) and see how it goes when you next switch it on :)
(I've noticed that you said it turns fine, once it's actually going round, so I'll assume there's nothing physically blocking its rotation).