This is a great question. Biologically speaking, there are some autonomous functions that do not require us to exert any will: for example breathing and heartbeats. All non-autonomous actions appear to be driven by motivation of some sort - hunger, thirst. Even when the motivation is to seek out positives - good food, good art, there is motivation. At the neural level, all thought and action are governed by action potentials and chemical feedback, driven by inputs whether immediate or stored.
Original thought might be an exception to that - sometimes I just get ideas randomly, or thoughts take random paths. Those are not motivation-based, but action on those is underpinned by motivation of some sort or the other. Admiring the beauty in the world is also not driven by motivation - the ability to recognize and appreciate that beauty is independent of motivation. Recognizing injustice - also not driven by motivation.
It seems, to me at least, that a world without original thought, beauty or justice would be an unhappy one.
Ergo, motivation is the answer for many things, but perhaps not everything. Maybe not even happiness.
> are we, humans, biologically limited by our own mind?
Indubitably. Teams do better than individuals at pretty much anything, even when physicality is not involved. Can you imagine an intelligence with greater capacity than human minds, and what it might be able to achieve? Look around us - civilization, society is proof that a superior intelligence (combined intelligence, in our case) can achieve more.