How do I motivate this student?

There is onestudent in my class who comes consistently, butt does not do any work. He loves to sit in class and draw. He is rarely disruptive or disrespectful. Initially I found myself repremanding him at least twice daily. Icouldtell that he was beginning to resent me, and my reprimands were accomplishing nothing. I decided to try a different approach because I did not want all of our interactions to be negative ones. I started greeting him (and others) when he arrived to class and asking him questions about his day or weekend. During class, rather than reprimanding him for drawing, I would take an interest in whathe was doing, but ask him to put it away and participate. When it was time to complete work during class I would ask him if he wanted help. I encouraged him whenever he did the slightest amount of work. This helped us develop a better relationship, but did not help motivate him to do work. This has gone on all quarter. Last Friday, the classwas working on writing business letters to people in the community who have power to change things that are unjust in the community. Students had been working on the letters for two weeks. They had chosen their topics, completed research on the topics, identified stakeholders, outlined the letter, and written a first draft. This student had not done any of the work. The day before starting the unit, I learned that the student had been harassed by the police in his neighborhood. The police stopped him and his friends because they looked like suspects of a crime. In addition to handcuffing the youth, the police drew their guns on them. My student did not seem traumatized by theevent, but he was upset about the way he and his friends were treated. I suggested that he write a letter to the police chief about the incident if he felt comfortable and safe enough to do so. Two weeks went by and he still had takenno steps to complete the work. On Friday I checked in with him while he was at his desk drawing. He told me he did not have a topic, and I brought up the incident as a possible topic. He said he was interested in the topic. I asked him to write down a sentence describing his opinion on the topic. I gave him a couple of minutes alone to do so, but when I returned, he still had blank paper and had returned to drawing. I then sat there with him, and asked him to verbalize his opinion tome. He did this. When I asked himto write it down, he hesitated. It seemed as though he may have a lot of trouble with writing. I am really ata loss as to how to help this student. I would like to sit down with him and work with him, but getting him to follow through has been unsuccessful. What should/could I do?