Convincing a programmer to work for a startup for 0 salary and 0 equity?

If there's no salary or equity being offered, the company wouldn't be able to sign a binding contract with the programmer, since they'd be offering them nothing in return for their work (no "consideration"[1]). Thus, there would be no "work for hire" agreement, and the programmer, not the startup, would own all the intellectual property they created.

Also, if it's a for-profit business, paying zero salary for useful work would be violating federal and state minimum wage laws (in the U.S.).

[1] https://en.wikipedia.org/wiki/Consideration

This question is less absurd than it sounds. You just need to find someone who is both talented and lucky enough to have already made all the money they will ever need to live on, and whose biggest challenge in life is that of finding something meaningful to do with their time. You get them to work for free by offering something they can't just buy: work they are personally interested in doing which is aligned with their sense of meaning. The pitch is that you will do the work they don't want to do, you will put together the support team and infrastructure they need, and in exchange for their time and experience you will be giving them an opportunity for autonomy and accomplishment which is greater than what they could reach on their own.

The secret many people haven't realized is that this situation effectively holds for talented programmers even when you are offering a salary: offering a salary broadens the pool of talented programmers who can afford to accept your offer, which is important, but it also clouds the issue by mixing in an extrinsic motivation for doing the work, which is not correlated with skill.