Have you used Publish Online for any previous projects? I ask because if you work for a large organization (or government agency) they may have this feature disabled. If not, I would go to your Creative Cloud desktop application and click on the icon in the upper right (might be your picture), and sign out and then sign back in.
Chad, the OP already tried that and I suspect if it was enterprise with it disabled, there'd be no button.
We need more details. Despite the "My Indesign CC is up to date" what is the exact version and build? What is the exact operating system? Do you have a second machine to try this on? Is this a personal account or a corporate account?