When I turn my ceiling fan on, it will be on the highest speed first, then when I pull the chain to lower the speed to medium, it stays on high, and when I pull the chain again to go to the lowest setting, it still turns on the highest speed, but when I pull the chain for the fourth time, it will shut off. So, when I pull the chain on the fan, it recognizes the different speeds but the motors keeps turning on high until I reach the off settings.

Sounds like the fan switch is kaput. Buy yourself another ceiling fan unless you know how to take the fan apart and replace the switch that's bad.

First of all, ignore the above answer.

What make/model is the fan?

It sounds like a bad capacitor. Easily replaced. See:

Ceiling fan capactors - troubleshooting and resources - Ceiling Fans N More