Windows 7 HomeGroup is a little troublesome.

I posted recently about HomeGroup which seemed to be a very positive feature of Windows 7 in that it allowed very easy to use, and secure, file sharing between computers on the same network using Windows 7 (any version).
My first attempt involved two desktop computers with wired internet connections through the same router.
Now I tried it between one wired desktop and a netbook (Windows 7 Ultimate) which was wirelessly connected to the internet.
The wireless netbook repeatedly gave the message "No Other Homegroup Computers Are Available" and no option to join a homegroup was available in Network and Sharing Options. As a result, I was completely unable to import files from the desktop.
However, connecting the netbook through an ethernet cable from the same router immediately made the homegroup on the desktop visible and I could easily transfer files from desktop to netbook.
I have seen forum posts complaining of the same problem when one of the two Windows 7 computers was wirelessly connected (couldn't locate any of them to link to this post, however).
I've also seen posts blaming AVGFree (anti-virus) for being "anti-homegroup" and recommended substituting Microsoft Security Essentials. Indeed, my desktop has AVGFree.
Many times the above error message arose because of firewall issues which are elaborated upon here. Could my problem have had anything to do with me having a FW on each Windows 7 computer IN ADDITION TO one on the router?