I'm not sure which pin leadfoot is talking about, other than the link arms that you said looked fine.
Most limp headlight issues are due to stripped plastic gears inside the operator gizmo.
Click here for the best brass gear replacement kit that I know of. Make sure you get the right version for your year car.
This thread has more info about the gears in posts 2 & 27. If you get Rodney's kit I linked to, it includes a metal bracket that goes over the plastic piece you have to glue back together, so the glue isn't the only thing holding it in place.
Normally if the gears are stripped you'll hear a grinding noise. Try raising the light by turning the manual operation knob. If you have a cordless drill and bit adapters, use that instead of your fingers. If you hear any grinding/popping, it's the gears. If it doesn't move at all, try raising it by hand while still turning the knob, I'm guessing you'll hear the grinding when the light is about half way up.
If it were my car, before ordering anything I'd pull out the headlight motor (just the motor & gear, not the entire headlight assembly), then take the plastic cover off to get a look at the gear.
Once you have the metal gears the problem will be solved (one brass kit = 1 side of car), but I firmly believe that the 'twighlight' feature of the C5 is what causes most of these problems in the first place. Sitting still it's fine, but just a few times of your lights turning on at interstate speeds and those plastic gears are toast.
