I had the same issue, and I resolved it without deleting files and database.
To show group avatar, Buddypress uses a setting from wordpress. When it is disabled, Buddypress won’t show your group avatar. So, in admin, go to Settings > Discussion and make sure Show avatars is checked in Avatars section (you can find it at the bottom of the page).
Once I checked it, avatars started to show on my site. I hope it will be the same for you.
