There is an organisation in Australia called Computer Bank that has been collecting and re-purposing computers for years. There are a number of international organisations that do similar things, some are listed here - http://www.computerbank.org.au/links.
You could also seek sponsorship from a hardware vendor such as Dell - http://www.dell.com/Learn/us/en/aucorp1/corp-comm/corporate-sponsorships, or even Google.
Since it needs to be shipped there, perhaps approach transport companies. Also, some technology recycling companies will supply equipment cheaply or free for the right cause.
Some organisations require that a not-for-profit organisation be established before funds are allocated. You'll have to check your local laws.
"If value corrupts then absolute value corrupts absolutely."