Please open regedit, go to HKLM\System\CurrentControlSet\Services\avast! Antivirus and delete the value called "Group". Then restart the computer and report if the change had any effect on the issue.
Ok I deleted the "group" value like you suggested, restart (using 4.7.981) The both icons are back and function properly. Yep. That seems to fix it.
Ok, I have to surrender to the facts, but it is still a fact that this issue happens (with me at least, at home and at work) even without Avast! installed. Well, I'll follow the clue listed here.