I read on here about going through free cycle. That doesn't work so well here in Indiana. One place we were able to find a free laptop is through the college classifieds online. It wasn't perfect and it was in Chinese, but it had a good system. I enjoyed learning enough Chinese to learn what control panel was.
Another place you could try is the for sale/free or the computer/electronics sections on craigslist. Definitely be careful, but sometimes you can find someone who just wants to get rid of an old computer.
Overseas, they had a program for students where they could get a solar powered laptop. There was a promotion where the company was raising funds to donate them. Also, as far as special needs, Easter Seals has a program for kids who, after evaluation, can get what they need.
One last note, research writing a grant proposal. I know this sounds bad, but if you can afford a smart phone, you can afford a computer.
Hope this helps.
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I just read about a computer grant you can apply to. I saw it on interconection.org, they also have discount on computers.