Upload & Sell: On
My personal philosophy is "free or full price." I have no problem making photographic "donations," for causes that I feel strongly about, for *very* good friends, or for access to subjects I wouldn't usually get to shoot. However, I've never liked the feel of "discount" photography. To me, the "discount" path cheapens the work far more than simply giving it away. Again, this is my personal philosophy on free/discount work. Others will have their own views/preferences.
If you do decide to donate, I would still include an invoice for your standard rates, which then reflects no charge. This is useful for both your financial records as well as your credibility as the artist.
Edited to add one important piece: you seem to understand this, but it's a common misperception that "non-profit" automatically means "no budget," and nothing could be further from the truth. There are big and small non-profits, with big and small budgets, just like any other business. The non-profit nature of the business should be irrelevant (except for your tax purposes, should you decide to donate your work).