The pull switch makes no difference in speed on all settings including OFF. There is a wall controller -- bypassed that; no change. Swapped light/fan circuits suspecting wiring -- no change. Swapped fans (happened to have an old one I just replaced but was working fine) -- no change. Having swapped everything but the house, I am confused as to what it might be.

SO.. . Any fan installed in this location runs slow? When you pull the chain to off the fan continues to spin?

What make are the fans (both of them) and the wall controller?

Both fans are Lowe's Harbor Breeze fans. There were in the house when we bought it and are about 5 years old. And, yes -- they run even when in the pull-chain off position. They change direction with the slide switch.

Wall controller was bypassed, but is a Hunter

The fact that they run even with the pullchains in the off position speaks to a pullchain issue, but then switching the fans would solve the problem, unless BOTH fans had a pullchain issue.

Try both fans in a different installation location (workbench is fine) and report on how they behave.

Tested the capacitor and switch -- both are working correctly. Some hum is now evident from fan.

Only thing to try is bypassing the existing electrical circuits but I would think that swapping the light/fan circuits would be equivalent.

Not sure what fixed the problem but suspect a bad connector. In any case, I installed the control unit I tested from the extra fan and it now works??

Wall control unit?