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I would undo the google search bar and see if it fixes the issue. If when you disable or unistall the google module it goes back to the way it was working you know that it is something associated with that google module.
-> tried. no able to get the [Groups] to work so not a fault of the google search.
Also you might want to see what file it's trying to access when selecting groups from the admin section and make sure that file is on your server.
-> the search is just plain html added to theme.html as i can't get to [Groups] to configure the settings.