Volunteering is a brillant idea. He'll be giving back and maybe even see some people who are worse off then himself. One way or another for his mental stability I agree he has to get off his butt.
My son was on house arrest with an ankle monitor for 7 weeks and only left a handful of times - usually just to go to drug court or church. I knew it was bad when he would get excited about going to court - you would have thought he was going to a party with his friends with as much care as he took to get ready. He was heading towards a major depression and even the court agreed that if we didnt get him placed in rehab soon that they may have to lock him back up for his own sanity.
I never got anywhere with the chores around the house - too easy to say no to Mom but he did do a little community service at a church and was happy to be out of here. One of the larger churches in my area had a program for this exact thing - they could do volunteer/community service and had meetings they could attend. You could always say he can earn his $10 a day by working so many hours as a volunteer.