Povertycoin? Don't give this alt coin devs anymore ideas, though I'm sure something like this has already been done or attempted anyway. I think if you create a coin just to be given away then it's pretty much worthless. People want to actually own or transact with it, but giving it away will just naturally devalue it. You could also just do something like this with bitcoin if you wanted to be completely altruistic.
Should that valuation prove reinforced sufficiently (say, by force of rhetoric), that valuation shall endure.
We do have such a coin, it's called "bitcoin".
Money is a store of wealth. It is not wealth so you can't just print money and be rich. Your idea of donating a mining machine might work, however. It would work because mining is a productive economic activity. The problem will be the donation. That is where the wealth comes from in your system and someone will have to give their wealth away to make it happen. If the new miner grows his/her business and expands or diversifies then you could help someone out of poverty.
It seems like a better idea is a micro-loan exchange that requires repayment if the business is successful. The hope of repayment with a little interest will bring much more money in the door, even if the primary motive of the investor is helping the poor.
"Money" stores not wealth but rhetoric therefor manifest.
