If you're approaching local firms, your pitch would be the same as for any donation. There are three ingredients: the prospect's Ability to give, their Affinity for your cause, and your Access to the prospect. So you need to 1) Find businesses that are likely to support your mission and have hardware to donate, 2) Refine your case for support (Why should they give to your cause in particular? How does your mission align with their philanthropic priorities? How will their donation help you meet your mission or help them meet theirs?), and 3) Find someone to open the door for you. If the business doesn't have a corporate foundation or a charitable gifts program, you might need to do some networking through your board, volunteers, other supporters, or civic organizations to find a connection.
But you don't have to restrict yourself to local businesses. Here's a
TechSoup discussion of hardware donation sources.
Also, check out
Gifts In Kind International. They're in the business of giving away hardware.
Last, subscribe to
TechSoup's hardware discussion forum. There are occasional offers there for donated hardware.
Someone in another discussion also suggested posting a request on craigslist, if they're active in your area.
Robert