The damaged construct is a golem-like creature that is missing part of his body. He appears in a magical construct puzzle room of Daemonheim. He needs to be fixed, and then he will open all doors in that particular room. You can make the body part (either an: arm, leg or head) by making it out of the rocks next to it with a hammer and chisel. In order to fully complete the puzzle, the player must have a sufficient runecrafting level in order to "imbue" the rock body-part.