The lights stopped working on our Harbor Breeze ceiling fan. I have disassembled the light fixture portion and found that both the remote and the pull switch seem to reliably produce a change of state, but there is never any voltage to the blue wire coming out of this odd little plastic box. The blue feeds the black harness to the lamps. It would seem I could remove the box and tie the physical switch's output directly to the bundle of black wires running to the lamps. Would removing the box cause any problems?

Yes it would. I appreciate it when someone tries really hard to fix things but sometimes you just got to know your limits. That funny little box is likely a capacitor. Ceiling Fan Capacitor

Thanks for the reply, but I guess the question should be updated to "What sort of problems will removing the capacitor cause?" I saw your response after I had removed the capacitor, and found that now the lights and fan seem to work fine from both the remote and the pull-chains. The cap seems to only be tied to the lamps, and I would guess it is there to help keep the power consistent so there won't be flicker or dimming if the light is at less than full brightness, which isn't a concern for us- we want on and off, even though we can still adjust brightness. Hell- I'd rather be able to disable the dim function entirely.

Oops- please see additional post. I think I commented wrong.