There are definitely other powers in Hamlet. Two or three are major, and should be addressed: the supernatural, ethics, and emotions.
The supernatural is pretty easy to see: the ghost of Hamlet's father shows up. This would be striking in our age, but at the time, the presence of a ghost was even more meaningful. It meant something was amiss in the spiritual structure of the world. (This can be seen when Hamlet hesitates about killing Claudius as well.)
Ethics is more slippery, but there is definite concern with doing the right thing.
Emotions, though, is stronger still. Hamlet is overcome by emotion. He's paralyzed in the "To be or not to be" section. Ophelia is so torn by emotions she goes mad. Claudius's emotions reveal his guilt, and so on.