Hi Willie!

To raise the final piece of the Yellow Statue,
Click to reveal..
it will require a trio of Master Scientists to research some plans for the final step. Drop a Master Scientist on the Science Board to draw new plans for the Yellow Statue. Enlighten 3 Master Scientists with the new plans and drop them on the Yellow Statue to finish repairs.

Charcoal (along with salt peter and red wood) can't be gathered until you complete Chapter 1 and begin Chapter 2.