When the service is running, and you go to the Network and Sharing dialog, HomeGroup in lower left corner, what options are available on that page?
Mine shows a "Create a homegroup" button. There is also a troubleshooter there which might help.
You do not say if you ever used a homegroup, but during an intall it is easy to create one because the option is a little deceptive. But if you leave the homegroup after one was started, it should go away, but it is always available.
Do you have any other computers on your network running a homegroup?