There are probably charities that do this, do a web search and see what comes up or contact a hospital they should have social workers that are familiar with programs. There are a lot of things out there but have not run across one specifically for donating computers.
Round Rock Area Serving Center, RR TX, is one resale place among a few others in this area. Research and contact similar resale places in your area. Most if not all have donations-to-clients-[case by case]policies in place.