In order for Homegroup machines to show up they have to be sharing some folders from the Homegroup. Remember that the machine you are viewing from won't show up on that list, just the other Homegroup machines in the network show up there.
But , surely , if that were a true description of what is likely to happen here then I would get the following :-
If looking at dtop from ltop and clicking on Homegroup icon on ltop this icon would "open " to show icon for dtop. That does happen OK.
If looking at ltop from dtop and clicking on Homegroup icon on dtop , this icon would "open" to show ltop. That does not happen. The Homegroup icon here does not "open"
So for the problem PC you would need to go into the sharing and permissions and allow at least one of the Homegroup folders to be shared. Sharing and Permissions
I did this action with the Documents folder on the dtop. I did not change the appearance of the Homegroup icon nor its ability to "open " to reveal the ltop.
I suppose its no big deal as I am still able to share the contents across the Homegroup. Its just that I'm curious at this difference between the Homegroup icon on both machines.Both these icons , by the way , have a litle "+" mark proceeding them which led me to believe that clicking this would result in the icon expanding . As I say , this happens only on one PC.
Other times you sometimes need to set certain services to automatic which should help make your machine appear on the Homegroup list of the other machine.
I found several of these services set on MANUAL by the way , but having set them all to AUTOMATIC hasn't changed anything here.