What are your longer term goals, how are you going go to pay your rent/bills, are you hoping that donations will do this are that you can built a reputation/experience and eventually go commercial?
I actually did a similar thing about 7 years ago for a year, worked at a charity that took in old equipment and passed it onto the community. I was surprised that there were quite a few people of all ages(mainly elderly) that were completely computer illiterate.
We generally had a small cache of hardware and would swap parts around to build half decent PC's.
As was said though your real problem is liability and new parts, if you took apart a laptop for example and shorted the motherboard it could cost you £150-300 for a new motherboard and then a few days to arrive. Where are you going to get new parts for cheaper prices what happens if you order the wronf part, what happens if the part your ordered is broken. You have no have no industry contacts for wholesale prices.
PC repair shops have a cache of parts in stock.
You could run into a lot of issues and people hate parting with money I'm afraid. It's an honorable idea however but you'd need a bulletproof disclaimer.
WE WILL TRY TO FIX IT BUT IF WE BREAK IT THEN TOUGH COOKIES!