We have a 48" ceiling fan Hampton Bay/Renaissance II/Model 129857.
After rotating properly for the last 3 years, it stopped rotating after trying to adjust sense of rotation for warm weather using chain #3. Now it only hums and turns slowly after being gently 'pushed'; after an hour or so it slowed down and started emitting a burned odor.
Any suggestions?
Thank you.

PROBABLY a bad capacitor. Have you opened it up, does the capacitor appear melted?

Ceiling fan capactors - troubleshooting and resources - Ceiling Fans N More (http://www.ceiling-fans-n-more.com/ceiling-fan-capacitors.php)