"I do not want to do anything."
Translation:Nie chcę nic robić.
Consulted with a Polish philology graduate - that doesn't really work. You cannot succesfully do "nothing". You can write "Nie chcę tego zrobić" (I don't want to do this) because that's some specific thing that probably can be accomplished.
You can write "Nic nie zrobiłem" (I did not do anything) because it has double negative, but not really this. In your example it's not really double negative, because the first negation negates "to want".
I think I follow here; that the z added to the verb implies a complete and total action? Also, when you hover over the english example for translation the Verb to do is first defined as zrobic - I was thinking without z at first but that I was wrong. The good news is that mistakes and these discussion boards are perhaps the most valuable learning tools ever!