What is the homeowner's liability for neglecting a dangerous rotting tree that damaged my property?

I informed a new neighbor of danger of a large tree falling due to fungus (rot) at the ground level as well as being overgrown and in need of a serious trimming. Neighbor had unlicensed contractor survey and then trim part of this tree (the part over their house) and was told by the contractor that the rest of the tree was fine. (I disagreed) After that the local electric utility came in and removed one of the major trunks as they said it was going to fall onto their lines. At the time of this removal I again spoke with the neighbor and requested that they do something about the rest of tree which could possibly fall onto my property. They refused, referencing the tree contractors advice. Three weeks later the tree did fall onto my property (Calm summer evening, dry conditions, fell due to rot at base) destroying a large building and contents. My insurance paid only about 50% of damages due to the building being an "Outbuilding" and the value was policy limited. The neighbors insurance has stated that they are not liable for the loss. My question is simple. Since the neighbor 1. Hired a unlicensed contractor and 2. Allowed the electric utility to remove a section of the tree due to the rot endangering their property, doesn't this show knowledge of the issue and therefore negligence on the part of the neighbor and should not they be responsible for the damages? Cleanup of the tree and building remains cost 50k alone. (Not covered by my insurance) The damages/contents shortage is in the area of 80k. Note: we both have the same carrier. Interesting case it seems. Thoughts?