I'd also second the thought that a balanced power conditioner like something from Equi=tech might be able to fix the issue. I'd also call a dealer and get their thouhgts. Cable Company carries a number of brands and has a lending system that I think includes power conditioners (it certainly includes cables and headphones).
What power conditioner will help in my situation?
The only power outlets I have are on the same circuit as the ceiling fan. When I change the fan speed there is a low frequency hum when I turn the fan speed from low to medium etc.
Aside from running a dedicated line, will a power regenerator or conditioner eliminate this?
Aside from running a dedicated line, will a power regenerator or conditioner eliminate this?