Hi Samir,
I used to volunteer pretty extensively with Free Geek. I'm not aware of any similar organizations here, or anywhere.
If you can say a little more about the specs and condition of the laptop, I might be able to give you a guess about its value. One of the important parts of the Free Geek model is that they have a pretty clear cutoff, where a great many of the machines they take in are sent immediately to recycling. I wish they more clearly published what their current specs are, which might help with questions like these, but it looks like they don't. But if, for instance, it's a Pentium III system that's banged up, the primary value would probably be in recovering valuable materials, and diverting toxic materials from landfills. It would take more time and money than the value of the computer to put it to any kind of use.
Personally, I've messed around with Ubuntu and Lubuntu on a pretty wide variety of laptops recently. Since ZAReason appears to be Linux-only, I'd imagine the hardware is pretty driver-friendly. My general take is that anything older than a Core2Duo processor is more trouble than it's worth; and there are plenty of Core2Duo machines available on eBay for like $50 or less.
If it's C2D or newer, I'd think about getting it set up to do basic web surfing etc., my choice would be Lubuntu, and find some person who needs it to give it to. Give them a clear list of what they should and should not expect it to do; for instance, you might want to tell them it will never be satisfying for use with Netflix or Flash-based games, but should be fine for webmail, and basic Facebook use. Just give them a basic idea of what they should and shouldn't expect from it.
This is a bit rambly, but hopefully helpful. Let me know if you have any other questions, I find myself geeking out on this stuff more than I should :)
Pete