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I would make sure that you're connected to online services. If you look at the hidden icons in the task bar there should be a little globe icon, when you hover over that does it say you're connected to ArcGIS Online and signed in?
Are you able to add an ArcGIS Online basemap to your map document from Add Data > Add Basemap?
What kind of data do you have in the map document?
Is it possible that you're signed into a public/personal account rather than an organizational account? Free public accounts do not have the ability to host services and would not give you a publish option when signed in.
Is your map document in layout view or data view? It needs to be in data view to publish.
You can either use the icons at the bottom of the data frame to toggle back and forth or go to View > Data View.