I'd move on right away, without a backwards glance. All else aside, if you did bring a laptop you'd be setting yourself up for more of the same. But this is not necessarily a criticism of the person doing the asking, and I believe it's important not to get too worked up about these sorts of requests/demands/expectations.
Local culture throughout much of Africa dictates that those with little are entitled to try and guilt trip or con those with a lot--it is done among Africans as well as between Africans and Westerners. In fact, people with a lot of money or possessions are expected to contribute something when asked by friends, acquaintances or (especially) relatives--that's just the way things work. Usually they bargain the amounts down to whatever they're willing to part with.
I feel totally entitled to decline to participate in this sort of dynamic, and I usually do. I just don't see any reason to get moralistic, much less to get upset about it. And I do expect that in situations where I've got an ongoing relationship of some sort with a local person, they are likely to feel genuinely resentful if I don't contribute some small portion of my obvious wealth, regardless of the facts of our stated arrangement. Again, this would be true were I a fellow African instead of an American tourist (or volunteer).
I'm also not opposed to bringing some small gifts for host families. Or, small gifts can be purchased locally; I sometimes print enlarged photos, then have them laminated, and these are always appreciated. Lots of people leave stuff behind for local friends or hosts--clothes, shoes, cameras--but I don't care for this approach.
Hope that helps.
Mark