Hunter Ceiling fan and the pull chain does not change the speed. The switch goes through all four settings on, on on off. Is more than the pull switch at fault?

Switch may be clicking, but not switching. Possibly bad switch. You could identify wires on fan switch(black-L, and so on), and test switch operation. If switch or capacitor not problem, then maybe shorted windings on fan motor. If stuck on high, maybe a fan control easy solution?

I am fairly certain it is a bad capacitor.

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