The $10k won't change that. Your cofounder leaving makes it even more likely your startup will fail. And that means that should the startup fail, your startup will have failed and you will have done the wrong thing.
On the other hand, if you disclose the status to the investor, the worst thing that can happen is that you walk away from a troublesome project with a potential future investor who sees you as a person of integrity. The best thing that can happen is exactly the same as the best thing that can happen if you don't disclose. And the odds of that best thing happening are improved because you don't have to waste energy on a web of deceit and because you have an ally who will talk well of you.
A person is only as good as their word.