To publish from ArcMap, verify that you have version 10.1 or greater. From the File menu, you should be able to sign in to ArcGIS Online. Then, you can open your MXD and publish it from the File menu>Share as. You publish to "My Hosted Services".
So on the item details page of the feature service, the edit button is grayed out? When you publish a service, it may take a few minutes to start the actual service, as the features have to be loaded in. How many features do you have? Perhaps you can share the feature service item publicly and post the URL here.
Thanks,
Mike