TL;DR - Installed a light kit in two existing fans that both used to work. Lights now work, fan hums, but blades don't spin.
Here's what I did:
Just moved into a house that had ceiling fans already installed (and controlled by a wall switch) but didn't have lights. The fans both worked fine. I thought "that's easy, I'll grab some light kits at Home Depot and install them." Pop open each of the fan assemblies, connect the blue and white wires, flip the switch...no lights. Still fan, but no lights.
Hmm, problem must be higher up. So I get into where the fan is mounted to the ceiling and sure enough, the blue wire for the lighting is tucked away and not connected to anything. Since there is only one switch per fan (no separate switch for lights), I connect the blue wire to the existing black wire connections, screw everything back together, flip the power back on and now I have lights but no fans. I can hear the hum of the fan on each of the three speeds, but blades don't spin.
I also did this to both fans. I did the first and tested it but really was just testing to see if the lights worked, I didn't think to re-check the fans at that point. So the problem exists on both. Based on what I've been reading it seems like it may be the capacitor in the fan assembly, but the fact that this happened to both of these when I installed the lights makes me think the fix might be more than "buy a new capacitor."
Also, if I disconnect the blue and black wires for the lights in the fan assembly the fans still do not work. I haven't tried disconnecting the blue and black up in the ceiling yet (it's a huge PITA to get up there) but I feel like disconnecting in the assembly should be enough to kill that circuit.
[UPDATE] FYI, the fans in question are Casablanca Airflow 1040 fans. I think this is the relevant manual. The blue lighting wire is also labeled "D1 Option" but I can't seem to figure out what that means.