Thanks very much for posting back. I have bookmarked that link, and I will go through it carefully. I believe I have already done most of the things, but I will check for sure.
One clue in my case is that in addition to the problem I mentioned with the blue icons, I have the fundamental issue that from my Windows 7 computer if I try to click into Network-->Win8ComputerName, I get the well-known "You do not have permission to access \\Win8ComputerName. Contact your network administrator to request access." This is outside of the Homegroup, just looking for basic permission to access the computer. I am thinking that unless I can clear that issue up, the Homegroup problems will continue. I guess I need to re-check all of the permissions on the Win8 computer and turn off any firewalls, etc., to see if that is the issue.