That's a sticky one that may require an attorney to answer.  The one thought I have is, is the culvert located within the right of way of the road, or is it outside of the road association's jurisdiction?  If outside, it might require the road association to acquire a "drainage easement" from the landowner in order to do anything about it.  See Title 23 § 3101 paragraph 5A.

You might also be able to use Title 17 §2802. Miscellaneous nuisances, which includes, among other things, that, "unlawfully diverting the water of a river, stream, pond or aquifer from its natural course or state to the injury or prejudice of others; and the obstructing or encumbering by fences, buildings or otherwise of highways, private ways, streets, alleys, commons, common landing places or burying grounds are nuisances." 

Also, Title 17 §2808. Alteration of surface water flow  might apply.  It says that, "Unreasonable use of land that results in altered flow of surface water that unreasonably injures another's land or that unreasonably interferes with the reasonable use of another's land is a nuisance.  An action under this section must be commenced within 3 years after the cause of action accrues."

That last sentence may be a problem.  Would the 3 years commence when that culvert was installed, or when the trees on top of it caused the culvert to collapse?

If blocking the culvert is going to send silt down into the watershed and into Highland Lake, you might be able to get your local Lake Association and/or Soil and Water Conservation District or even the DEP or NRCS (Natural Resources Conservation Service) to step in and put some pressure on them.  They may know of other enforcement powers that could be used to protect the watershed.